Yes, but we can't get anywhere near the speed of light. Don't forget that you have to expend an equal amount of energy at the other end to slow down and stop as you needed to accelerate up to your not-even-remotely-close-to-light speed.Four and half years at the speed of light!
Give or take a couple of months!
Hundreds of years for a small group of us to reach the next habitable planet and it is a one way trip, most likely.
Ain't no sign of warp drive, yet. You have to overturn Einstein, first and that ain't been done yet.