I'd scrape the texture a few inches off on each side of the bad tape joint. Then fill on the joint with Multi purpose drywall compound. Let it dry, sand smooth.
Then pick up a texture brush. Home Depot has them for under $10.
I like to use a scrap piece of drywall and then add a bit of water to some joint compound. Test is with your brush. Dab it in the compound, then dab the brush lightly to the scrap piece.
If the texture is too heavy, add a little more water.
Do this until your texture on the scrap piece resembles the ceiling. Then dab away at the ceiling.
It's going to be hard to match it exactly, cause everyone has their own technique, and the mud will likely not be mixed exactly the same consistency as the original installer, but it'll look a HELL of a lot better then what you see now.
Don't get discouraged if it doesn't look exactly right. It takes a skilled drywaller to match texture perfectly.
If the ceiling is painted now, you will need to prime the patch well, then paint the whole ceiling. If you don't prime it, the paint will flash and you'll see exactly where you did your repair.