Can I use spackling to repair this damage between wall and celing?
Forget the spackling.

Fiber joint tape should never be used in a corner - use Paper Joint Tape instead. It has a seam down the middle, so you can fold it into the corner.

Scrape out the old joint tape, removing any loose compound along the way. Ensure both surfaces are securely attached, to their framing members. Sand any high spots if needed and apply paper joint tape in it's place.

You can use an Inside Corner Trowel to aid in making a smoother joint, while having fewer steps between coating and drying.

If it is a long run, you don't have to do it all in one shot either.

90 minute Lightweight Setting-Type, works great for repairs like this, due to a stronger joint, and quicker turn around while working. You just mix up what you need, and as long as you keep the remaining unmixed powder dry, you can store it for quite a long time.