Yes, but I would not use this in a formal essay for class and only sparingly in any professional writing. "And" is a conjunction which like the other conjunctions (but, for, nor, so, yet) is primarily intended to join two different sentences together into one, or to compare two ideas (as I just did here). However, if you open any book or read any article, you will probably see "and" and the other conjunctions at the start of sentences. Even so, many English teachers will forbid the use of conjunctions to start sentences and may mark you down for it, and there are two good reasons for that. Using "and" to start a sentence gives the writing a very informal tone because it sounds more like speech, and English teachers are generally trying to move students away from informal writing to teach them a more professional way to communicate. Secondly, using "and" is a bit lazy and tends to be a bit imprecise. Here are some better alternatives: moreover, additionally, therefore, comparatively, and furthermore.