Usually, no.
The college should have all the equipment you need.
Anything you may need to add to that - they will make very clear at the start. If you know what college you are going to, ask them about it now - it's a fair question.
Perhaps they may encourage you to get your own. But you should not be penalised if you don't.
Not everyone has the money for it, for one thing.
In this internet age, it's not such a bad idea, though, for students to have a computer of some sort. They are good tools for researching information, preparing assignments and presentations, taking notes, etc.
But you can just as easily do this with a notebook and pencil, plus a home computer, or one at the school - and it does not have to be all that fancy, either.
Some teachers (I say teachers, not schools) like assignments to be printed, and score higher for this - very bad policy and very poor teaching.
Of course, if you are studying computer technology, you will want a laptop, for sure.
I know of one Primary School in New Zealand that has tried to make a particular brand of IPad compulsory. Half the families cannot afford them. It stinks.