That is a horrible idea. Leaving aside the fact that the squirrel is a wild animal and shouldn’t be in a cage shalalala I’m going to tell you why it is NOT a good idea from my experience.
My brother decided he wanted a squirrel, he set up a trap. It was not a sofisticated one, only a cage with a stick on the entrance and food inside. We let him do it, thinking no squirrel would fall for it, but we were so very wrong. A couple of minutes later we heard screams so we went outside to find TWO squirrels trapped inside my brother’s cage. The squirrels were doing so many painful noises, there was blood everywhere surrounding the cage because they were attacking each other. We decided to let them free, but we couldn’t get near the cage because they would try to bite us. They were CRAZY! And I don’t blame them, I can only imagine how terrified they were. We moved our cars as near as possible to the cage and with the windows as closed as possible we used some large sticks to open the cage’s door. Needless to say it was not a fun experience, plus the squirrels ended up getting pretty hurt.
No matter how cute a squirrel might look, unless they were previously domesticated or were born and raised by humans, they are wild animals. Imagine catching a rat that was running in front of your house. Catching a squirrel has the same risks of getting an animal who might be sick, even with rabbis, just with a fluffy tail and cute face, than when you catch a rat. Plus, the squirrels bite and VERY hard.
It is going to be much more pleasant for you and the squirrel to find some place where squirrels are living and feed them. It is fun to watch them eat. 

(Source: perfectbucketlist)