Inclusion Criteria:  Willingness and ability to sign the study-specific informed consent form Willingness to comply with all study procedures and attend all study visits. Participant with (a) B-cell malignancies or (b) AML (CD117 positive) who are undergoing allogeneic SCT at Penn State Cancer Institute from an 8/8 matched unrelated donor. Donor selection and screening criteria are to comply with 21 CRF Part 1271. Male or female participant, age ≥ 18 and ≤ 75 years. Ability to swallow oral medication. Women of childbearing potential (WOCP) as defined as not surgically sterile or not postmenopausal must have a negative serum pregnancy test at screening and a negative urine pregnancy test within 7 days of beginning the condition regimen. Men and WOCP must agree to use 2 medically accepted method of contraception and must agree to continue use this method while on the trial and through at least one week after the last dose of study drug. Acceptable methods of contraception include abstinence, barrier method with spermicide, intrauterine device (IUD) known to have a failure rate of less than 1% per year, or steroidal contraceptive (oral, transdermal, implanted, or injected) in conjunction with a barrier method. Periodic abstinence (e.g., calendar, ovulation, symptothermal, post ovulation methods) withdrawal, spermicides only, or lactational amenorrhea are not acceptable methods of contraception. WOCP must use a medically accepted method of contraception and must agree to continue use this method from the time of signing the informed consent through at least one week after the last dose of study drug. Karnofsky Performance Scale (KPS) equal to or greater than 70%.  Exclusion Criteria:  Renal dysfunction with eGFR <30/mL/minute/1.73 m2 by Cockroft-Gault formula. Participant requires warfarin or vitamin K antagonist within one week of acalabrutinib administration. Participant requires treatment with a strong cytochrome P450 3A inducer or inhibitor. Treatment with post-transplant cyclophosphamide Treatment with any other investigational products within 21 days of conditioning regimen. Known hypersensitivity to acalabrutinib, tacrolimus and methotrexate and their excipients. Active uncontrolled infections Human immunodeficiency virus (HIV) positivity. Hepatitis B or C serologic status: subjects who are hepatitis B core antibody (anti-HBc) positive and who are hepatitis B surface antigen (HBsAg) negative will need to have a negative polymerase chain reaction (PCR) and must be willing to undergo DNA PCR testing during the study to be eligible. Those who are 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 to be eligible. Those who are hepatitis C PCR positive will be excluded. Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of study procedures. Diagnosed or treated for another malignancy within 2 years before study registration or previously diagnosed with another malignancy and have any evidence of residual disease. Participant with non-melanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone resection. Participant with coagulopathy or bleeding disorder. Known hepatic cirrhosis or severe pre-existing hepatic impairment (ALT and/or AST more than 3x greater than upper limit of normal, Total Bilirubin more than 2x greater than upper limit of normal) Uncontrolled high blood pressure (i.e., systolic blood pressure > 180 mm Hg, diastolic blood pressure > 95 mm Hg). Uncontrolled or symptomatic cardiac arrhythmia Left ventricular ejection fraction (LVEF) < 40% as assessed by echocardiogram or radionuclide angiography, or NYHA class 3 or 4 heart failure Myocardial infarction within 6 months of signing consent. History of stroke or intracranial hemorrhage within 6 months of signing consent. Breastfeeding or pregnant. Has difficulty with or is unable to swallow oral medication, or has significant gastrointestinal disease that would limit absorption of oral medication. Suspected or confirmed PML(Progressive Multifocal Leukoencephalopathy) Requires treatment with proton-pump inhibitors. (Participants receiving proton-pump inhibitors who switch to H2-receptor antagonists or antacids are eligible for enrollment.) FVC, FEV1, or DLCO (corrected with hemoglobin) less than 40% of expected value. Prothrombin time (PT)/INR or aPTT (in the absence of lupus anticoagulant) >2x ULN. 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. Concurrent participation in another therapeutic clinical trial.