There are three main Apertium service implementations:
apertium-service, see Apertium-service, a multithreaded C++ XML-RPC/REST/SOAP server, using apertium as a library
ScaleMT, see ScaleMT, a multiprocess Java XML-RPC/REST server, starting apertium language pairs as new processes
apertium-apy, see Apy, a multiprocess Python 3 tornado http server, starting apertium language pairs as new processes
ScaleMT and Apertium-service are in need of some maintenance, but Apy is well-maintained, pretty easy to install, and is currently used for https://apertium.org. If you want to run a translation server yourself, just install some language pairs and run Apy, it's pretty simple. Or, if you're lazy, you can use our server, more info at Apy.