There isn't a way to do that directly. You have several options.
- Click on the sketch in the tree and Ctrl+C to copy it, and then open the Part file, select a plane or face (assuming it's a 2d sketch), and Ctrl+V to paste it. The internal dimensions and relations will stay with the new sketch, but any relations or dimensions to elements outside this Part won't carry over, so you'll need to edit the sketch and add relations or dimensions as needed to fully define it in the Part. If you're editing the Part within the Assembly you can reference other components. After closing the new sketch you can delete the original sketch in the Assembly.
- Edit the Part within the Assembly, create a new sketch on the same plane or face as the Assembly sketch (or one that's parallel to it), and use the "Convert Entities" sketch tool to reproduce the sketch entities in the Part. If you use this option you will of course need to keep the sketch in the Assembly instead of deleting it, unless you first delete the "On Edge" relations.
- Just chalk it up to experience, delete the sketch in the Assembly, and re-create it in the Part. It's good practice, and it should go faster the second time.