Oh sure. The hardest part will be matching the wall texture and the paint colour.
Before you do anything else, remove the large pieces of broken plaster carefully so as not to break them if at all possible. You want to be able to take the biggest ones to the paint store to get a computerized colour match. That's your best bet at matching the paint, so please don't throw them away.
From the looks of things, that's a plaster wall.
The first thing you need to do is figure out how to remove the towel rack from the fasteners that are still trying to hold it on to the wall. Look on the underside and around the base of the end pieces for set screws that hold the "cones" to the larger diameter round bases. Typically, the round bases will get screwed to the wall and the "cones" will hook onto them and get secured in place with set screws.
If you come up empty, phone around to the hardware stores in your area and ask who the major hardware wholesalers in your area are. There's a good chance the someone at the wholesalers will be able to recognize that rack and know who manufactured it. The manufacturer's sales rep will know how to remove it from the wall.
If you still come up empty, then try to get that towel rack off as best you can, and if you end up wrecking it in the process, then new ones aren't very expensive.
Judging by the way the plaster is broken, the towel rack was probably mounted with hollow wall anchors.
After you get the towel rack off, maybe post a close up (that's in focus) of the screws (or whatever) that were holding the towel rod on. Different hollow wall anchors look different, and you'll need to either remove the anchor from the wall, or let it drop into the wall, depending on what you have.
After that, the best next step in my view, (and I hate to say this) is to buy yourself a bag of base coat plaster from any drywall wholesaler in your area for about $15. I personally like Perlite Admix Hardwall made by the Georgia Pacific company. I think it's about the best base coat plaster available. But...
Base coat plaster is what you need to repair plaster walls, and a bag of it will last a newbie forever, and take up about as much space as a Saint Bernard all during that time. I know people will use Polyfilla to repair plaster walls, but I have no experience whatever with Polyfilla, so I really couldn't advise you of how to use it properly in this repair. An option might be to simply buy a shopping bag full of base coat plaster from any drywall or plastering contractor in your area for $5.
You'll also need some white wood glue. 2 or 3 fluid ounces (50 to 75 milliliters) of it will be plenty.
PS: Nice fish.