Can you activate Singularity if I have only one unit?

Yes, you can activate (play) Singularity if you have only one unit.

According to the official RiftJudge FAQs (specifically FAQ #9075, #8602, and #5969), the phrase "up to two units" means you can choose to target 0, 1, or 2 units. You are not required to have two targets available to play the spell, nor are you forced to target your own units if you do not want to.

If you choose to target only your one available unit (or an opponent's), that unit will simply take 6 damage.