Generators in ARK currently do not snap to existing electric cables. However, they can still be connected to existing cables, as demonstrated in this video: Youtube. To successfully do this, the following steps must be taken:

• Align the generator ghost such that the end of the cable is touching the snap point and the generator is at a valid angle (must be parallel or perpendicular to the cable)
• Place the generator
• Remove the cable you 'attached' the generator to
• Replace the cable

This is trickier to do with vertical cables, as they get in the way of placing the generator. Furthermore, restoring power to vertical/inclined cables appears to be buggy. It seems to work reliably for normal straight cables though.

The snap point of the generator is shown at the end of the video and in the image to the right. You may wish to practice in singleplayer before risking resources doing this online. As shown in the video, this can be used to power a circuit with redundant generators.