Whenever you have custom API developed and choose it as a Function, it will be treat as GET function and by right should work via browser.
The format is https://<orgurl>.crm5.dynamics.com/api/data/v9.0/<api_name>(<request_header>=@p1)?@p1=%27<value>%27
You can also use the tool – Custom API Tester in XrmToolBox to perform the testing.
But please bear in mind whenever working as Function, you should consider the URL length as the limitation.