I have not done it myself on an Android device, but it seems possible.
It's not an "app" per se, so you need to be handy with the terminal.
According to
https://trac.ffmpeg.org/wiki/HowToBurnSubtitlesIntoVideo
ffmpeg -i video.avi -vf subtitles=subtitle.srt out.avi
That requires you to have ffmpeg compiled with libass support.
To compile ffmpeg, follow this guide:
https://github.com/guardianproject/android-ffmpeg
or this:
https://trac.ffmpeg.org/wiki/CompilationGuide/Android