It seems obvious that Terminators don't have vocal cords, and their speech is probably generated by some kind of speaker assembly linked to a speech processor. However, every time we see a Terminator speaking, it moves its mouth just like a human would. In most cases, this is presumably because they want to appear to be human, and speaking without moving your mouth is a rare talent and, if a Terminator did it, they would raise suspicion.
But there is at least one scene, in the first movie, where the Terminator is alone in his apartment, where no one can see him, and the landlord comes to the door and complains about a bad odor coming from the room. The Terminator replies in terms that I won't repeat on this family friendly site. The issue is that when the Terminator replies to the landlord, who - as I have said, can't see him - the Terminator's mouth moves.
Note: The dialogue in this clip is probably NSFW
If moving his mouth wasn't a necessary part of his speech process, he has no reason to do it in this scene. He doesn't need to keep up appearances when no one can see his face.
Humans speak by a combination of muscle movements: the diaphragm draws air in and forces it out of our lungs, after which it passes through the larynx, where the vocal cords shape the sound, and finally, the air passes out through our mouths, where our lips, and especially tongues, put the finishing touches on the sounds we are producing. But Terminators don't have lungs, larynxes, or vocal cords. So how do movements of the mouth and tongue affect their speech?
This raises the question of whether the bare metal Terminators (see picture below) can speak, and if so, whether their mouths move when they speak. They certainly don't have lips or tongues, so those can't play any part in the process.