American Right to Family Act This bill requires the cancellation of removal and adjustment of status for an alien parent who meets certain requirements. To be eligible for cancellation of removal and adjustment of status under this bill, an alien must (1) meet certain residency-related requirements, such as having been physically present in the United States for at least 10 years or having received a deferral of removal under the Deferred Action for Childhood Arrivals policy; (2) be a parent of either a U.S. national or an individual who first entered the United States under 16 years of age and has been continuously present in the United States since entry; and (3) not be barred from receiving certain immigration benefits on specified grounds, including certain grounds related to criminal conduct or national security. The Department of Homeland Security may waive certain crime-related grounds of inadmissibility for reasons related to the public interest, subject to various limitations. An alien whose removal is canceled under this bill shall be adjusted to temporary resident status for a three-year period, which may be renewed. Furthermore, a cancellation for removal or adjustment of status under this bill shall not count toward certain annual numerical limitations on such actions.