NO not really. First of all in almost every state deer are strictly regulated because they can carry some of the same diseases as cattle. And as a "wildlife" hunting species, in general you would be required to have a permit in order to confine the deer in the first place.
In order to acquire the deer in the first place, you have to buy them from an approved dealer, you have to have a permit and appropriate fencing. Appropriate fencing is either one 8 foot fence surrounded closely by a second 6 Ft fence or an even higher since fence to prevent escapes.
Finally you have to have the deer tested for TB, and CWD, and a few other diseases. Depending on the state you live in, you have to have "permission" to "import" them from a different state. and basically jump through ton's of hoops to finally get a few to your place at some great expense.
And lastly, you DO NOT want to attempt to hand tame any bucks. Bucks that are handled as young and hand tamed are downright dangerous in most cases. Doe's on the other hand are very nice as hand raised animals.
No it is not possible to ride a deer ( if you mean either white tail or mule deer) because neither is really big enough or well suited temperment wise for riding. I've however seen both Moose and caribou put under harness and used to pull a cart or wagon. But again you have to raise them from babies, have the appropriate knowledge and skills to deal with their flight instincts and you have to have the appropriate permits to keep the animals or face time in jail.