You could write a script using the strtotime() function. I would suggest storing the date in the unix timestamp format.
<?
mysql_query("select * from <table>");
while ($details = mysql_fetch_array($query))
{
Convert the timestamp
$unixtime = strtotime($details["date"]);
Write values back
mysql_query(update <table> set date='$unixtime' where key='$key');
}
?>
When this has done all records, and only then, change the column type to timestamp.
NOTE: you may want to test the use of this function before operating on the live database! It does some weird things sometimes!