I can’t seem to find the thread someone posted dealing with a similar issue, but I believe either a spray on or roll on texturing product was recommended. Maybe you can Google while you wait for someone with experience to weigh in.

It looks to me as if someone mixed sand with joint compound, then dragged something through it randomly to make those tracks.... something like a straw broom. I would buy some joint compound, add some sand, and use cardboard as a base to practice recreating the texture.

Ha-ha-haa, there would be no need for professional drywallers if greenhorns could tell one another how to match texture. That picture doesn't reveal much detail but if I had to guess I'd say crow's foot brush.

well, these comments served the purpose of bumping up the post, giving you the chance to weigh in and the OP another avenue to pursue in fixing their ceiling! ;)