Refuge From Cruel Trapping Act of 2021 This bill prohibits, with specified exceptions, the use or possession of body-gripping traps in the National Wildlife Refuge System. The bill imposes on persons who possess or use such traps in the system (1) for a first offense, a civil fine of up to $500 for each body-gripping trap possessed or used; and (2) for subsequent offenses, a civil fine of up to $1,000 for each body-gripping trap possessed or used, imprisonment for up to 180 days, or both such a civil fine and imprisonment. The bill makes any body-gripping traps that are possessed or used in violation of this bill, and any wildlife captured by the use of such traps, including the pelts and raw fur, subject to civil forfeiture. Persons found to be in violation of such prohibition shall pay all associated court costs.