Of course yes!
I haven’t heard of a college that doesn’t allow it’s students to own a Mobile phone. Actually, the student is required to have a Mobile phone of his/ her own that is registered during admission procedure as his/her.
In fact in some links on the intranet of the college, the student mobile phone number is necessary to login.
It’s required to contact anyone, be it your family, friends or teachers since using a coin box (a rare thing these days) would be extremely difficult and vexing.