Yes there is a such a thing as time travel. Every person alive is TRAVELING THROUGH TIME as in going forward with our daily lives! A day is a unit of time. We travel through time at a rate determined by the physical laws of the Universe.
I suspect you mean can we travel forwards at an accelerated rate or backwards in time. Well, within the confines of the physical Universe so far it appears that travel BACKWARDS through time is NOT possible. Of course Physics is a branch of science and science IS provisional so IF some aspect of Time Space is discovered making it possible then the theories will be amended to match the laws we come to understand - as we experience and learn them and NOT assume or have a prophet proclaim without being able to test and falsify the theory.
Travelling FORWARDS in time has ALREADY BEEN ACCOMPLISHED! YEAH!!! Albert Einstein postulated that as you accelerate TIME AROUND YOU IS SLOWING DOWN in effect everyone around you is standing still and YOU are getting to the future FASTER! Relatively speaking. This was tested by putting an atomic clock on a rocket and accelerating it around Earth and then comparing it with an identical clock that remained on the planet. There was a testable and verifiable difference between the two clocks that corresponds to Einsteins postulate establishing it as theory. Postulate/conjecture is the idea, hypothesis is what Einstein accomplished the VERY FIRST time his mathematical model worked out. The moment other mathematicians verified it his hypothesis became a theory and once it was test and demonstrated to actually work within physical reality it became established as -- still just a theory comprised of other theories that all explain the way the Universe can be UNDERSTOOD to work - at least within the limited thinking and VERY LIMITED mathematical modeling language of a group of apes called humans that happen to be living on a pale blue dot called Earth.