Some effect on time? Time is relative for everyone. Time is not one thing, there is not one timeline or so. So yes it affects time in that a moving entity progresses slower in time than one who stands still in respect to the moving entity.

But we all move with the rotation of the earth, rotation around the sun, our sun through the galaxy, and the galaxy through the universe with unimaginable speeds. The funny and mindboiling thing is that everything is relative. Whichever way you move (faster than our current speed, or "slower" when you move the other way) you always end up moving slower through time compared to your starting point.