A collet will hold the part more accurately. That being said, I made my own adaptor plate for my rotary table to mount a chuck. I had a spare chuck I took off my mini lathe when I updraded it to a bigger chuck, so I just made it to fit. It was pretty simple for me as the chuck already had a centering register machined in the back. If you have a piece of metal you like laying around you can do it easy enough on your own. It was easier because my chuck was smaller than my rotary table, but you could make a two piece or screw together plate if you needed to for a larger chuck.
I just used mine as an indexer on my 3 axis machine, but it could just as easily have a stepper or servo motor added if I wanted to use it as a true 4th axis.
I used aluminum because its what I had handy. I'm not to worried about flex due to its thickness. Obviously a piece of cast iron or machineable tool steel would not have to be as thick, and still be much stronger.
I did everything except machine the back keys on the adaptor plate manually on my lathe or on my manual mill. I probably did not need the alignement keys as I mounted it with four bolts and machined it to fit, but I would have had to spend more time centering it when I remounted it after attaching the chuck if I had not put them on there. Now I can take it off and put it back on and be within a few thousandths right away every time. I don't ever plan to take it off again, but you never know.
Chucks can be had from tons of places new and used.