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.
It’s better if the student owns a smart phone since the internet facilities in it help a lot in accessing the college website without having to turn to your laptop (which is also allowed ;)).
But, you are not supposed to use phone while in class during a lecture for quite obvious reasons.