[Credit & Copyright: Dan Durda (FIAAA, B612 Foundation)]
Of course, catch it in a tractor beam.
Ion Drive sounds great, and this concept would work, if you could just build the ship right in front of the asteroid.
Otherwise, getting the ship ‘to’ an asteroid, and then getting it ‘parked’ in front of it, might require a bit more than an Ion Drive.
Another challenge would be trying to alter the ‘course’ of an asteroid. Although possible, it would take a really, really, really, long time.
Why don’t they just drive an anchor into the asteroid and attach a rope to it ?
If you can deflect an asteroid FROM Earth, you can deflect an asteroid TOWARD Earth.
My cousin Marvin’s tow truck could do this for less money. The asteroid has to be in neutral, though.