The easiest way to do this is by exporting and re-importing all your records as a csv.
Export all your records, making sure to include the record ID in the export. You don’t have to export all the field, just the field that will become your date field.
Be sure to back up your database before importing in case things get messed up, you’ll be able to restore it.
Once you’ve got your exported CSV, change your field to a date field.
Before importing, be sure to select the record ID field as the “match field” and that a matching record will be updated by the imported record. This is very important. When you import the CSV, the text will be converted to a date and update the field in the record.
Understand that there is a limit to what the date parser can do. Dates must be complete, the years must have 4 digits and the format should match the date format used on your site. If you’ve got a mix of different formats, you may find that some of them don’t get converted correctly.
