My Linux knowledge is very limiting, but you could give them 'sudo' access
# visudo
add the specific user in the visudo configuration file
add the specific command, crontab (with full path - maybe /usr/sbin/crontab???), in the visudo configuration file
all the user has to do is type
then input their user password, and voila! They should be able to run it.
OR, I might be completely wrong.