Putting records in a specific sequence

I'm prototyping an app that will allow users to change the sequence of records in a list, i.e., prioritizing tasks. The table has a "Sequence" field that is a number, but that can be changed if needed.

Ideally, the UI would let users grab a record in the list, drag it to where they want it in the list and then drop it, but I don't think that is possible.

I'm looking for ideas on how to implement a slick way for users to re-sequence records.