Supplementary answer expanding on @PearsonArtPhoto's answer.
The first part of getting ISS (or anything else) from LEO to the Moon is lifting it's orbit around the Earth (or at least one end of its orbit) until it reaches the Lagrange point between the Earth and the Moon (EML1). The delta-V requirements for this are on wikipedia. Using "high thrust" (a conventional rocket or similar doing all the work in a short period this needs about 3.77 km/s of delta-V. Using low thrust, like ion engines, about 7 km/s.
We can use the rocket equation
$${\displaystyle \Delta v=v_{\text{e}}\ln {\frac {m_{0}}{m_{f}}}}$$
to tell us how much propellant we'd need. For the high thrust option, using liquid hydrogen and liquid oxygen $v_e$ is abotut 4500 m/s and we get about 2.3 for the ration of the original mass to the mass delivered. So we'd need a bit over 500 tons of propellant to lift the ISS there. In this case the thrust would be high enough that we'd also have to worry about the ISS falling apart while we pushed it.
Using a xenon ion engine we have $v_e$ about 40 km/s, so the mass ratio needed is about 1.2 and we'd need 80 tons of Xenon, plus quite a lot of power generation and ion engines if we wanted the initial thrust to be enough to overcome air resistance. Apart from other problems, that is about 2 years world production of xenon and would cost about a hundred million dollars.
It may be possible to save a bit of delta-V by exploiting the interacting gravity of Earth, Sun and Moon, but it adds still more to the time taken.
Once we get to L1, it's easy, in a sense to get to the surface of the Moon. A small push in the right direction will do it. On the other hand it will get you there at about 2.5 km/s (about 5000 miles per hour) so there won't be a lot of usable components to recover from the new crater. Decelerating from that velocity can't be done with a low thrust system (you need enough thrust to hover on the Moon, which is about 700 kN for the ISS).
So you definitely need a chemical rocket engine for that final stage. Assuming you can somehow keep hydrogen liquid that long, you would need (rocket equation again) about 300 tons of propellant. On other words you need to deliver 700 tons of EML1, which then means that you needed about 900 tons of propellant (or 140 tons of Xenon) to get there from LEO.
So that's just the physics. From an engineering standpoint, most of the rockets and other systems that would be needed for this don't exist and would have to be designed, built and tested, before being launched to ISS. Which might be fun, but would be very expensive.
What might be feasible is simply to raise ISS's orbit to an alitutde where it would be stable for a few centuries, say 900km where the materials would be available just in case we want them for something.The Delta-V for that is about 300 m/s and could be achieved by something like a SpaceX starship with no cargo configured as a tug.