NASA launched Lunar Orbiter Program in an effort to map Moon's surface, choose landing spots for Apollo missions and acquire images for landing simulator. Did USSR have similar program? Luna 12 seems to fit the criteria but it was only one mission. Were there any other attempts?
I am assuming that the point of the question is Soviet imaging of the Moon, and not strictly lunar orbiters.
There were, in fact, two Soviet programs which included spacecraft with the task of imaging Moon's surface. First was the Luna program, which you found yourself. In this program, the stations that managed to get images of the Moon from the orbit were Luna-3 (quite low-quality images of the far side), Luna-12 (the ones you saw), Luna-16 (it was a sample-retrieval mission, but it sent several photos taken during the flight) and Luna-22. Several other craft, for example, Luna-11, failed to achieve the right orientation and ended up with their cameras pointing away from the Moon.
Second was the Zond program. Spacecraft of this series were testbeds for several other programs, but several of them did a flyby of the Moon.
You can find photos of the Moon taken by Luna- and Zond-series Soviet spacecraft here (most photos need to be clicked to get the full image). Sadly, most of Soviet archives are still hardcopy-only and there are no official online repositories.