The simple answer is, sadly, no. People are still unsure as to what gravity actually is, but it seems that it is either the interchange of particles (dubbed `gravitons`) between objects to cause a force (in the same way that particles are exchanged in electrical attractions between, say, protons and electrons).
The other possibility is that gravity is a `warping` of the space occupied by a massive body (most noticable with a star or planet, though gravity is still exerted by small objects).
So when a small body gets close to, say, a star, the warping of space means that the object `falls` toward the star (just like rolling a ball down a hill, but, confusingly, in three dimensions).
So a photon in a beam of light travelling toward a star falls down this well, altering its direction, just like any other object.
Gravity`s effect on time is wierder though, but think of it like this. We`re talking about space bending, so lets bend some stuff. Start with a piece of paper. Assume it has no thickness, just length and width, and then bend it. As soon as you start to bend it, you introduce a third dimension, height. It is impossible to bend a two dimension shape without adding a third dimension.
Now think of bending a three dimensional shape - not just changing its shape, but in the same way that the paper was bent (don`t try too hard, because it gives you a mean headache). It can`t be done without adding an extra dimension - time. So, in warped 3d space, the warp is FOUR-DIMENSIONAL! So the gravity warp has an effect on time.
Its really difficult to describe something you can`t see, but I hope this makes just a little bit of sense...