Assuming you have this finger app installed. My Android store does not seem to have one, for example.
It's just a shell function so in this case if one had a terminal app that has a shell one could add the function. No idea how feasible that is on a phone.
If it has a shell and telnet/nc it has finger:
echo user | nc example.com 79
Lynx works too over gopher:
lynx gopher://graph.no:79/0/london
[dead]
Finger is a protocol. It's older than IP.
You can read about it in RFC 742.