Short answer: yes.
(Sorry, English teachers—welcome to the 21st century.)
You most certainly can start a sentence with a coordinating conjunction—it's simply a matter of style and formality.
Let's take a few steps back.
Coordinating conjunctions join together other words, phrases, or clauses that have similar constructions. You can remember them using the acronym FANBOYS: for, and, nor, but, or, yet, so.
These FANBOYS should look totally familiar to you, but starting a sentence with them? Maybe not so much.
However, if you are writing in an informal tone, starting a sentence with a coordinating conjunction is a useful means of drawing attention to a sentence and giving it a little more oomph. You don't want to overdo it, though, because it might sound like you're trying to deliver a punch line. But feel free to place one at the beginning of a sentence every now and again. See what we did there?
P.S. If your teacher disagrees with us, do whatever they tell you to do. And then send them to Shmoop for a life lesson in "common usage."