Blocking Rioters and Insurrectionists from our Cities to Keep us Safe Act of 2021 or the BRICKS Act of 2021 This bill increases criminal penalties for rioting and related offenses (e.g., inciting a riot). First, the bill increases from 5 to 10 years the statutory maximum prison term for a rioting offense. Second, it establishes higher statutory maximum penalties for rioting offenses that involve certain aggravating characteristics. Specifically, it provides a prison term of up to 25 years for a rioting offense that results in serious bodily injury or includes a dangerous weapon, explosives, or fire; and a prison term of any years or for life for a rioting offense that results in death or includes kidnapping, attempt to kidnap, aggravated sexual abuse, attempt to commit aggravated sexual abuse, or attempt to kill.