Can we capture it?
For any two objects in orbits around a common body (like the sun) to match their orbits, they need to have their locations match and their velocity, at the same time. To collide, you only need your location to match.
One way to do this is to get to a matching location and then do a hard change of velocity so that the asteroid is now in a stable orbit. But that's a lot of energy for a rock with a mess measured using scientific notation.
There are better candidates out there where we could make a tiny change to their orbit and have them be captured naturally due to relative velocities being much closer to matching. Still a lot of energy, but a lot less.
Once you know how much dV is required to capture, we'd next need to put that much dV at the object, which would be even more costly to launch.
Lastly, depending on the object's composition it may not be possible to even apply much dV to it. If it's a essentially a coalesced pile of rubble, any force applied will just break it into pieces. If it's roughly solid, then maybe.
Fun fact: Earth has had more than one "moon" in the past, they just tend to not last long before they're kicked out of orbit. [0]
https://cneos.jpl.nasa.gov/sentry/details.html#?des=2023%20D... says its speed will be roughly 11 km/s (were Earth not present) and an impact velocity of 15km/s (were Earth in the way; Earth's gravity speeds things up).
If we do that with rocket power, and not some complicated gravity-assist path, then we can look at New Horizons. That used an Atlas V rocket at around 570 tons to get the 478 kg payload up to 16 km/s. That's a 1:1000 mass ratio.
Once you've caught up, you've got to turn things around and slow down. But you're talking about another 1:1000 or more mass ratio, leaving you with a few grams of material.
This is all hand-waving to give a rough idea of the problem.
We've had a few asteroid sample-return mission. Hayabusa2 returned a few grams of material from 162173 Ryugu. The hope is that OSIRIS-REx will return 60 grams from 101955 Bennu this fall. These used ion thrusters (more efficient than chemical rockets) and atmospheric braking to help slow down.
Still, none of this is anywhere near being useful as construction material. It would be far cheaper to bring it up from Earth.
That's not enough to use as building materials.
On the less humorous side it would probably be pretty hard to impart enough delta-v to capture it.