How to specify a editor to open crontab file? "export EDITOR=vi" does not work

To quote the man:

The -e option is used to edit the current crontab using the editor specified by the VISUAL or EDITOR environment variables

Most often if you run crontab -e from X, you have VISUAL set; that's what is used. Try this:

VISUAL=vi crontab -e

It just worked for me :)

Very probable that your VISUAL environment variable is set to something else. Try:

export VISUAL=vi