Run this from the branch where you want the file to end up:
git checkout otherbranch myfile.txt
General formulas:
git checkout <commit_hash> <relative_path_to_file_or_dir>
git checkout <remote_name>/<branch_name> <file_or_dir>
Some notes (from comments):
myfile.txt
and mydir
an alternative:
git show commit_id:path/to/file > path/to/file