Yes, but only a certified technician can legally do it. Under EPA rules in 40 CFR Part 82, Subpart F, issued under Section 608 of the Clean Air Act, anyone who maintains, services, or repairs equipment that could release refrigerant into the atmosphere must hold Section 608 Technician Certification.
The rules define a technician as anyone who adds refrigerant to or removes it from an appliance, or who attaches hoses and gauges to measure the pressure inside it, so recharging a refrigerator falls squarely under the requirement. EPA offers four certification types, and Type I covers servicing small appliances, a category that includes refrigerators and freezers designed for home use under EPA’s Section 608 definitions. Technicians earn certification by passing an EPA-approved test given by an EPA-approved certifying organization, and the credential does not expire. Apprentices are exempt only while a certified technician closely and continually supervises them. For most homeowners, that makes a refrigerator that needs refrigerant a job for a certified repair technician rather than a do-it-yourself fix.
Source: U.S. EPA, Section 608 Technician Certification Requirements
Image: Embraco refrigerator compressor, Ente75, CC0, via Wikimedia Commons.