No, direct access to the API is currently restricted to System Admins, would get fairly complicated to let a Power User do it since I would imagine you would want their rights to follow through on which API’s they could or could not use.

There are ways to let users perform actions leveraging the API and iframe embedded content, but you have to program it out and basically build a mini-application for the task for the user to do.

Remember, the primary goal of the API Browser is more documentation than production usage, it’s nice that it can be actually used, but not really its goal.