No. Dolphins are very large, so you would have to have a huge aquarium to keep one in, and dolphins need to be in large groups to be happy. A dolphin would be a good friend - leave it in its natural habitat and you go visit the dolphin!
Recently many scientists have recommended that dolphins, whales and porpoises be reclassified as "non-human persons." A bill of rights has even been drawn up for these people that would protect them from murder as well as being owned by people or corporations. Basically, if you own a dolphin you own a person, and that's just not right.