Yes, photons have energy, and anything with energy causes gravitation.
More precisely, photons have a non-zero stress-energy tensor, which is what acts as the "source" of gravitation. See, for example, this Wikipedia page:
The stress-energy tensor of a source-free electromagnetic field, down the page, would apply to photons.
I add this qualification because there are also cases where an "energy" can be assigned to the gravitational field itself, but this "energy" is not part of the stress-energy tensor and so it does not act as a "source" of gravitation in the above sense.