That looks more like a miscut section of drywall than a misalignment. Meaning there may be a relatively big open area behind that gap.

The caulk recommended previously is still the better fix, but it may be a bit of a chore to keep the bead from opening up as you smooth it.

Before I saw the answer, I had bought DAP Crack Shot High Performance Spacking Paste from the HD. I think the spacking paste is to patch damages on the drywall, right? Can I use the spacking paste to fill the gap between a door frame and wall?

You can use spackling paste, but it won't be as flexible as the caulk, so the crack might reopen somewhat in the future.

You could be creative and put an extra molding around the door frame, problem solved.

Krissie

if the gap is too big to caulk
use a backer rod to fill the gap first
then caulk over the backer rod.
you can find different sized backer rods
@ builidng supply stores.
spackling will dry and crack
caulk allows for expansion and contraction.

best of luck

Thanks for your advice. By the way, is the caulk just the silicone? I saw GE Silicone II for door and window from the HD. Is that the right one to fill the gap between the door frame and wall?

You need siliconized acrylic/latex caulk (not silicone caulk).

Look for painter's caulk that is siliconized, which gives it more flex.

I'm with Krissie put another piece of moulding over it. Perhaps a 14/ round piece added to the top of the door. If this is an aesthetic repair, IMHO filling a gap like that with flexible caulking won't look good.

That being said, if it's not aesthetic (you can't see it normally but need to get on a tool or something to see the top of the soor frame) then what difference does it make? Leave it and forget about it.

Lastly, you could remove the top molding, cut out a piece of the drywall and replace with a piece that will fit nicely to the frame, finish the drywall joints, paint the wall and replace the molding.

"filler" is not a good solution. Just my 0.02.

Judging by the picture, unless you are Wilt Chamberlain, you aren't going to see the filled gap. Dap dynaflex or alex plus caulk. It will take two applications as the first pass will shrink. Make the second the cosmetic pass smoothing both passes with a damp finger as mentioned above.
Lay out the first run, then laying your index finger as flat to the top of the casing as possible, work it into the open areas. Let that cure for awhile, give it a day, then run a second bead using the same method. Dampen your finger keeping a damp rag or paper towel handy.

I believe that the small gap you show in your picture will disappear when it is caulked. Just make sure you have a paintable caulk in case you want to paint it. You sound inexperienced, but don't worry as this is a simple fix. While it's hard to lay down a smooth bead of caulk without experience, the technique described above using a moist finger or paper towel in a swiping motion will do the trick. And if you lay down too much latex caulk, you can clean it off with a wet towel if you do it right away.