Carbon Capture Improvement Act of 2021 This bill authorizes the issuance of tax-exempt facility bonds for the financing of qualified carbon dioxide capture facilities. A qualified carbon dioxide capture facility is any equipment installed in an industrial carbon dioxide facility that satisfies specified capture and storage requirements and (1) is used for the capture, treatment and purification, compression, transportation, or on-site storage of carbon dioxide produced by the industrial carbon dioxide facility; or (2) is integral or functionally related and subordinate to a gasification process that converts a product from coal, petroleum residue, biomass, or other materials that are recovered for their energy or feedstock value into a synthesis gas composed primarily of carbon dioxide and hydrogen for direct use or subsequent chemical or physical conversion.