Photons have no rest mass.
But the quantity that determines how a thing gravitates, or responds to gravitation, is not rest mass.
It is a complex entity called the stress-energy-momentum tensor that consists of energy, momentum, pressure and shear stresses. (It is usually represented by a 4 times 4 symmetric matrix. It is not a simple number.)
Now it so happens that for most everyday objects, their speeds are small compared to the speed of light, and pressure and stresses are also small compared to relativistic mediums. So the stress-energy-momentum tensor is dominated by rest mass. When it comes to the Sun, the Earth, a lump of metal, a human being… gravitational behavior is very accurately (but not perfectly!) described using Newtonian gravity and their respective rest masses.
But the moment we get to relativistic speeds, this is no longer the case. Entities can no longer be characterized by rest mass alone; other components of the tensor become equally important.
In particular, a photon has no rest mass, but it carries plenty of energy, and it has momentum. Its stress-energy-momentum tensor is certainly not zero. So it can be a source of gravity, it has inertia, and it responds to gravity. But its behavior can no longer be described by Newtonian gravity, as evidenced, among other things, by the fact that relativity theory predicts (correctly, as confirmed by observation) twice the deflection angle for a photon in a gravitational field than the deflection of a Newtonian particle would be, moving at the same speed.
also read:speed of light explained