Now since Photons have energy too, is it possible for these particles to gravitationally attract each other.
Photons are not "particles", in the sense that they are not objects. They have some particle properties, that are referenced as such in order to do calculations and make predictions treating the photon as if it were a particle. The photon is the unit or quanta of the redistribution of the electric field when the source or sources of the field move. As such, it doesn't make any sense to think of this as an object, the photon and the electromagnetic wave is just a mathematical description of this realignment.
It is certainly possible for electromagnetic waves to interfere with one another, but this is very different from gravitational attraction.