Absolutely, use the UNIX / Linux command scp (secure copy):
$ scp user@server:directory/SourceFile TargetFile
Update based on OP's response:
$ scp path/to/my/file.txt user@server.com:/path/to/copy/to/file.txt
Question
I'm using a Mac to remotely access a computer in my university's computer lab. The Mac serves as a terminal. If I need to transfer some files from my computer into the one in the lab, is it, firstly, possible? If yes, then please guide me to it.
Solution
Absolutely, use the UNIX / Linux command scp (secure copy):
$ scp user@server:directory/SourceFile TargetFile
Update based on OP's response:
$ scp path/to/my/file.txt user@server.com:/path/to/copy/to/file.txt