Inclusion Criteria:
* Men and women ≥ 18 years of age
* Moderate-severe chronic GVHD, diagnosed per the 2014 National Institutes of Health (NIH) criteria
* Progression or recurrence of active chronic GVHD signs/symptoms after treatment with steroids
* Karnofsky performance status \>= 70%
* Woman of childbearing potential (WOCBP) who are sexually active must use highly effective methods of contraception during treatment and for 2 days after the last dose of acalabrutinib
* Men must refrain from sperm donation during the study
* Willing and able to participate in all required evaluations and procedures in this study protocol including swallowing capsules without difficulty
* 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:
* Hospitalization for evaluation or management of an infection within the last 8 weeks
* Change in immunosuppressive regimen within the 2 weeks prior to enrollment
* Noncompliance
* Treatment of chronic GVHD with ibrutinib
* Received any investigational drug within 30 days or 5 half-lives (whichever is shorter) before first dose of study drug
* Recurrent or 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, or other cancer from which the subject has been disease free for \>= 2 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 on study
* Has difficulty with or is unable to swallow oral medication, or has significant gastrointestinal disease that would limit absorption of oral medication
* Received a live virus vaccination within 28 days of first dose of study drug
* Known history of infection with human immunodeficiency virus (HIV)
* Uncontrolled, active significant infection (e.g., bacterial, viral, fungal or progressive multifocal leukoencephalopathy)
* Known history of drug-specific hypersensitivity or anaphylaxis to study drug (including active product or excipient components)
* Active bleeding, history of bleeding diathesis (e.g., 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 warfarin or equivalent vitamin K antagonist
* 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 30 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
* 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
* Child-Pugh score of C for hepatic impairment
* Total bilirubin \> 2 mg/dL or alanine aminotransferase (ALT) \> 2 x upper limit of normal, unless abnormalities are due to liver GVHD, in which case total bilirubin \> 3 mg/dL or ALT 5 x upper limit of normal are exclusions
* Absolute neutrophil count \< 1.0 x 10\^9/L or use of myeloid growth factors within the past 2 weeks
* Platelet count \< 50 x 10\^9/L or platelet transfusion or thrombomimetic agent within the past 2 weeks
* Glomerular filtration rate \< 50 mL/min/1.73 m\^2
* Breastfeeding or pregnant
* Concurrent participation in another clinical trial and receiving a non-Food and Drug Administration (FDA) approved medication