Basic easy method:
Take a #10 by 1.5" brass flat head wood screw and silver solder or braze it to the butt plate (not soft solder). Drill a 1/4" hole in the antler for the screw to fit into. Fill the hole with good epoxy, also covering the end of the antler. Put on the butt cap and clamp in place to cure. As the epoxy sets, wipe off any excess with a cloth wet with denatured alcohol. Let cure for a day and then slowly shape the butt cap to fit the antler. Don't get it hot or it will loosen the epoxy.
Prior to this, fill the pith by applying cyanoacrylic resin ( super glue) repeatedly to make it harder. The accelerator spray works well in this type situation.
The reason you don't want to use soft solder is that in shaping and polishing the solder easily melts and the butt cap comes off.
Slightly advanced method:
A really good looking butt plate on a stag handle is a threaded through tang with an acorn nut. That may not always be possible, but the same look can be done with a fairly simple method.
Preliminary steps. Sand the antler butt flat and square. Make it at the angle you want the butt to be. When satisfied, use a ball burr and relieve the pith about 1/8" below the outer rim. This make sure there is an epoxy reservoir under the butt cap as well as making the fit between the rim and the cap snugger. I do this on the front and back of all hidden tang handles.
Once the butt is ready, fill the pores of the pith with CA as above. You don't have to do this, but it is just good craftsmanship.
1) Cut a 3" piece of 1/4-20 threaded rod. You can use brass or steel, depending on the acorn nut you will be using. You can cut off a long bolt if you don't have any threaded rod around. The size that looks good is 1/4", but #10 will work for smaller knives. This is your butt cap stud.
2) Drill a .200 pilot hole in the center of the antler butt, trying to keep it close to perpendicular. Run a 1/4-20 tap down the hole. Put epoxy in the hole, and screw in the stud about 1.5" deep. Simplest way to run in the stud is to chuck the end in a cordless hand drill and slowly run it down the hole. You only need to grip the end 1/2" of the stud in the drill chuck, and if the drill damages the threads, just cut off any damaged threads after the epoxy cures. Leave about 3/4" of clean thread exposed. File/grind the end clean so a nut will go on.
You now have the equivalent of a threaded tang sticking out the antler butt.
3) Cut the butt plate a bit oversize, and drill a 1/4" hole for the stud. Place on the stud and use a nut to make sure it sits flat on the antler. Mark the perimeter of the butt on the plate and remove. Trim to a close fit, leaving a little to file away after glue-up. When all is good, fill the butt with epoxy and place on the cap. Secure with a temporary nut. Remove the nut before the resin fully cures, but after it gels. Shape as above.
4) Make an acorn nut - There are many types that are pre-made, but it is really simple to shape a piece of low carbon steel or a chunk of damascus rod into one. You don't need a lathe. Just tap the metal to match the stud, put on a cut off bolt and lock in place with two nuts. Chuck the bolt in a hand drill and shape the nut on the belt grinder. Clean up and fine tune any shape with files and sandpaper. You can also start with a section of a threaded coupling.
Shapes for acorn nuts are as varied as pretty girls faces. You can sculpt them, make them geometric, or plain and rounded ( the acorn nuts, not the pretty faces).
More Advanced:
A knife with matching low layer count damascus fittings makes a nice knife into a show winning knife. This does not need to be expensive or difficult. If you forge, or have a friend who does, making a simple practice billet of damascus is fairly simple. A simple small billet is a great learning task and will produce a piece of damascus that will make the guard, butt cap, and acorn nut. Make it from nine pieces of 1X6X1/8" metal. I recommend 15N20 and 1084 as the alternating metals ( 4 and 5 pieces respectively). I won't give a welding tutorial here, but the process is to weld up the billet good and solid, and work it into a roughly 1X1" square bar. This is your low count billet. It can be used as-is, or folded and reduced to make a higher layer count (20 or 40). If you have some prior welding skills, it can be forged round and twisted ( a very good look), then made into the pieces needed.
Make the billet and when done, cut and forge it into the pieces you will need for the knife parts.
You need a 1" long piece for the acorn nut, a piece of 1/4" thick flat for the butt cap ( 2"X1.5" is a normal size), and a piece for the guard of sufficient thickness and length ( this can vary a lot, but 1/4" is the minimum thickness). A sculpted guard, incorporating the guard and bolster in one piece, is easy to forge the basic shape and finish on the grinder or mill and with files. I like it to be about 3/4" to 1" thick at the bolster area and end up around 1/4" at the quillion/guard ends. The same effect can be made by stacking 1/4" pieces of damascus and putting a thin contrast piece in between them ( 20 gauge nickel silver is good). Look at photos of some knives by the big guys and you will get many ideas for this.
Make the acorn nut as above, having the layers show in laminated side view if the billet was just stacked and welded. If the billet was twisted, it looks better done in the lengthwise round alignment ( a slice of the round twist bar).