Of course you can! You have to grant root permisson. Read the ln manual pages.
MySQL stores the database data in separated dirs in
/var/lib/mysql. I think, at first you had to make a dir, where you want to put the selected database's files.
Grant root permisson, stop MySQL deamon:
# /etc/init.d/mysql stop
Copy your data to your new folder:
# cp /var/lib/mysql/DATABASENAME /path/to/new/database/dir
Remove your old dir from MySQL data files: (Warning! ALWAYS make SQL dump first!!!)
# rm -R /var/lib/mysql/DATABASENAME
Make a symlink back to MySQL data dir: (Pay attention! Read the man page of ln first!!!)
# ln -s /full/path/to/new/database/dir /var/lib/mysql/DATABASENAME
After it, you are ready, start your MySQL:
# /etc/init.d/mysql start
Warning! If your new dir isn't write- and readable by MySQL that wouldn't work!
Example, the common problem: you place your new data dir to your home folder, your home folder is read protected by others(ex: drwxrwx--- you you yourdir).
Ask, if you want to know other things about that method!