Inclusion Criteria:

          -  Subjects must have a biopsy confirmed newly diagnosed CD20 positive B cell PTLD.

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0-2. ECOG 3 will be
             permitted if the decline in performance status is due to lymphoma. [See Appendix 1]

          -  Subjects must have adequate hematologic, hepatic, and renal function as defined below:

               -  Hemoglobin ≥ 8 gm/dL

               -  Absolute neutrophil count ≥500/mcL (unless documented bone marrow involvement
                  with lymphoma)

               -  Platelet count ≥50000/mcL (unless there is documented bone marrow involvement
                  with lymphoma)

               -  Prothrombin time/international normalized ratio (INR) or activated partial
                  thromboplastin time (aPTT) (in the absence of Lupus anticoagulant) < 2x ULN.

               -  Total bilirubin ≤1.5X upper limit of normal (ULN)

               -  Creatinine ≤2.5X upper limit of normal (ULN)

               -  Alanine aminotransferase/aspartate aminotransferase (ALT/AST) < 2.5 X or ≤5X ULN
                  for patients with document hepatic involvement with lymphoma

          -  Women of childbearing potential and men must agree to use adequate contraception
             (double barrier method of birth control or abstinence) during treatment and for 12
             months after last dose of study treatment. Women who have undergone surgical
             sterilization or who have been postmenopausal for at least 2 years are not considered
             to be of childbearing potential.

          -  Subjects must be willing and able to participate in all required evaluations and
             procedures in this study protocol including swallowing capsules without difficulty

          -  Subjects must have the ability to understand the purpose and risks of the study and
             provide signed and dated informed consent and authorization to use protected health
             information

        Exclusion Criteria:

          -  Prior treatment with any BTK inhibitor

          -  Subjects receiving any other investigational agents or participating in another
             therapeutic clinical trial.

          -  Subjects with active (treated or untreated) brain metastases/ central nervous system
             (CNS) disease (including but not limited to CNS PTLD) will be excluded from this
             clinical trial

          -  Prior malignancy (or any other malignancy that requires active treatment), except for
             adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer,
             early stage prostate cancer or other cancer from which the subject has been disease
             free for ≥ 3 years

          -  Clinically significant cardiovascular disease such as uncontrolled or symptomatic
             arrhythmias, congestive heart failure, or myocardial infarction within 6 months of
             screening, or any Class 3 or 4 cardiac disease as defined by the New York Heart
             Association Functional Classification. Subjects with controlled, asymptomatic atrial
             fibrillation during screening can enroll in the study.

          -  Has difficulty with or is unable to swallow oral medication, or has significant
             gastrointestinal disease that would limit absorption of oral medication.

          -  Known history of infection with HIV. HIV-positive subjects on combination
             antiretroviral therapy are ineligible because of the potential for pharmacokinetic
             interactions with acalabrutinib.

          -  Patients with uncontrolled concurrent illness like active infection (eg, bacterial,
             viral, or fungal) requiring IV antibiotics or psychiatric illness/social situations
             that would limit compliance with study requirements

          -  Known history of drug-specific hypersensitivity or anaphylaxis to acalabrutinib or
             rituximab (including active product or excipient components).

          -  Active bleeding, history of bleeding diathesis (eg, hemophilia or von Willebrand
             disease).

          -  Uncontrolled AIHA (autoimmune hemolytic anemia) or ITP (idiopathic thrombocytopenic
             purpura).

          -  Requires treatment with a strong cytochrome P450 3A4 (CYP3A4) inhibitor/inducer

          -  Requires or receiving anticoagulation with warfarin or equivalent vitamin K
             antagonists (eg, phenprocoumon)

          -  Requires treatment with proton pump inhibitors (eg, omeprazole, esomeprazole,
             lansoprazole, dexlansoprazole, rabeprazole, or pantoprazole). Subjects receiving
             proton pump inhibitors who switch to H2-receptor antagonists or antacids are eligible
             for enrollment to this study.

          -  History of significant cerebrovascular disease or event, including stroke or
             intracranial hemorrhage, within 6 months before the first dose of study drug.

          -  Major surgical procedure within 28 days of first dose of study drug. Note: If a
             subject had major surgery, they must have recovered adequately from any toxicity
             and/or complications from the intervention before the first dose of study drug.

          -  Hepatitis B or C serologic status: subjects who are hepatitis B core antibody
             (anti-HBc) positive and who are surface antigen negative will need to have a negative
             polymerase chain reaction (PCR). Those who are hepatitis B surface antigen (HbsAg)
             positive or hepatitis B PCR positive will be excluded. Subjects who are hepatitis C
             antibody positive will need to have a negative PCR result. Those who are hepatitis C
             PCR positive will be excluded.

          -  History of progressive multifocal leukoencephalopathy (PML)

          -  Breastfeeding or pregnant. Pregnant or breastfeeding women are excluded from this
             study because it is unknown how acalabrutinib and rituximab can affect the fetus or
             infant. Rituximab can cross the placenta and is found in breast milk. Acalabrutinib
             has been found in the breast milk of animals and there is not significant data
             regarding its effect during pregnancy.

          -  Vaccination with live virus vaccines is not allowed within 4 weeks of study treatment
             of or during treatment.