Developer Radek Cervinka has an unofficial conversion of the Synapse TCP/IP library for Delphi XE6 Firemonkey which runs on Android and IOS. Indy is the default TCP/IP library that ships with Delphi XE6 and Synapse is an open source library available on SourceForge. The version on SourceForge does not run directly on mobile so this unofficial version has code changes that allow it to compile. There is a Firemonkey demo that comes with the unofficial version that demonstrates a few functions like HttpGetBinary and HttpGetText in addition to the NTP component which comes with Synapse. Some other useful functions I see in the source code are HttpPostBinary, HttpPostUrl, and HttpPostFile. Lukas Gebauer originally developed Synapse and you can find out more about it from it’s website here. Over on the main site of the official version there are more demos and howto documentation. Chances are probably pretty good that it will also work on Windows and OSX. It should also compile with minor or no changes in Delphi XE5 and AppMethod.
Head over and check out the full blog post from Radek and then download the unofficial Synapse TCP/IP library for Android and IOS.
Or download a mirror of the unofficial library here.