Free Modern URL Shortener.
Kutt API is a free URL Shorteners API that requires apiKey authentication, is served over HTTPS and supports CORS, so it can be called from the browser.

Unified API suite · now live
Geocode an address, validate an email, track a flight or pull stock data with one account, one dashboard and one API key.
A simple link obfuscator/shortener
Yes. The Kutt API is listed in the URL Shorteners category of the public-apis directory, which only includes APIs that are free or have a free tier. Check its documentation for rate limits and paid plans.
Yes. The Kutt API uses apiKey authentication, so you need to register for credentials before making requests.
Yes. The Kutt API supports CORS, so front-end JavaScript can call it directly.
Yes. The Kutt API is served over HTTPS, so it's safe to use in production.