Yes, this is possible. The device that makes this possible is called a polarizing beam splitter, which will transmit or reflect light according to its polarization. Thus, it will split diagonal or circular light into its horizontal and vertical components, and when used in reverse it will undo the process (it has to).
Note, however, that you will in general require a pretty exceptional interferometric stability to achieve this. You certainly require both beams to originate from the same source so that they have a definite phase relationship to each other; you would split the beam in two, polarize it in different directions, add a delay stage to control the relative phase, and then combine them using a polarizing beam splitter. The thing is, though, that you need the relative delay to be very tightly controlled, as a few tens of nanometers of difference in the path length will change the polarization from diagonal to circular. This is essentially doable but it is and fiddly, and requires very careful alignment - but that is optical physics in a nutshell.