mol.la is a free, open-source URL shortener. Creating a link needs JavaScript, but the API does not: POST https://mol.la/api/v1/links with a JSON body such as {"long_url": "https://example.com"}.
POST https://mol.la/api/v1/links
{"long_url": "https://example.com"}
See the developer docs, the OpenAPI spec, or llms.txt.