Build Better Borders Act of 2021 This bill increases a civil penalty for improperly entering the United States and appropriates the collected funds for certain uses, including for the construction of a barrier along the U.S.-Mexico border. Specifically, the civil penalty for an alien apprehended while entering (or attempting to enter) the United States at a time or place other than as designated by immigration officers shall be $450,000, or $900,000 for an individual who has been previously subject to the penalty. Under current law, the penalty is between $50 and $250, or between $100 and $500 for an individual who has been previously subject to the penalty. The bill appropriates the funds from such penalties for use by the Department of Homeland Security, and the funds may only be used to (1) plan, design, construct, or maintain a barrier along the U.S.-Mexico border; and (2) purchase and maintain necessary vehicles and equipment for the U.S. Border Patrol.