There are a whole range of options, if we have enough warning and invest in the technology[1]. My personal favourite is the gravity tractor:
> One more alternative to explosive deflection is to move the asteroid slowly over a time. Tiny constant thrust accumulates to deviate an object sufficiently from its predicted course. Edward T. Lu and Stanley G. Love have proposed using a large heavy unmanned spacecraft hovering over an asteroid to gravitationally pull the latter into a non-threatening orbit.
And the same technology could be used to actively "capture" asteroids for fun and profit
> One more alternative to explosive deflection is to move the asteroid slowly over a time. Tiny constant thrust accumulates to deviate an object sufficiently from its predicted course. Edward T. Lu and Stanley G. Love have proposed using a large heavy unmanned spacecraft hovering over an asteroid to gravitationally pull the latter into a non-threatening orbit.
And the same technology could be used to actively "capture" asteroids for fun and profit
[1] https://en.wikipedia.org/wiki/Asteroid_impact_avoidance