You'll need to do some coding to actually create the script. Actually, if you're really smooth with SQL, you may find you just need to write one update SQL query, but you'll need to be very comfy with MySQL string functions since you would have to parse the date and convert into a datetime value (which off the top of my head is formated as: 2004-01-21 15:01:01).
Or you could create a PHP script that loops through all your records and gets the date value. Then use PHP's [man]date[/man] function and maybe even [man]strtotime[/man] to convert the date into "Y-m-d H:i:s" (I believe this is the format you'll want to use to insert the time into the datetime field.
Granted, the PHP method is the slower of the two, but since you only need to do this once (versus as a regular feature of your app), speed isn't that much of an issue unless you have a gazillion records.
If you go with the PHP route, only test with 1 record until you get it right. Then unleash your recordset loop to handle all the records. Same may go with doing the SQL - unless you keep backups and don't mind restoring the data...