set the_file to choose file
set the_text to (do shell script "cat " & quoted form of (POSIX path of the_file))
set the clipboard to the_text
or alternately using only AS:
set the_file to choose file
set the clipboard to (read the_file)
(This second piece of code throws an End of file
error for me for certain files and I'm not sure why, so I'd use the first one)