The ISS has been pushed in the past by Zvezda's two small thrusters (nowadays inactive it seems) and more often by a Progress docked at the back of Zvezda. However the nozzle of the Progress can't gimball to aim to the station's Center of Mass. This center can't possibly be aligned with the center line of the main module axis nowadays, given the many things asymmetrically docked or attached in at least two axis. So how is a reboost performed without giving the station a massive angular momentum?
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The attitude control thrusters on the Russian Segment fire to maintain attitude during reboosts.
...the Russian Segment system provides the necessary thruster capabilities to handle reboosts and attitude control situations beyond the capabilities of the CMGs.
The International Space Station - Operating an Outpost in the New Frontier Chapter 7
In order to perform a reboost, attitude control of the vehicle is handed over from US segment CMG control to Russian segment thrusters control...
(CMG stands for Control Moment Gyroscope)
answered yesterday
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$\begingroup$ Your answer seems to imply that a spin in indeed induced, but that the thrusters in the Russian segment fire furiously to counter it while the push maneuver is ongoing. Wouldn't that generate massive inertias in all the other hanging masses? The entire thing could break apart. $\endgroup$ Commented 11 hours ago
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3$\begingroup$ @MisterSmith You mean massive forces. And no, the boost is very gentle. A typical boost takes about a minute and pushes the ISS by only a few meters per second. youtube.com/watch?v=CsZUkrGGfuo - the space station's push is the opposite of how you see the man drifting down the hallway. As you can see the acceleration is very little. It has to be, so it doesn't break anything apart. $\endgroup$ Commented 10 hours ago
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1$\begingroup$ Why would the forces preventing rotation be bigger than the forces induced by the big engine in back that's actually doing the reboost? $\endgroup$ Commented 9 hours ago
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3$\begingroup$ I don't see the word "furiously" in my answer anywhere. That comes out of your head. Firing thrusters doesn't "generate inertias". Inertia is a property of matter. The ISS is big and floppy, everything is done gently. When the Shuttle used to reboost it, it used 24 lbf jets. space.stackexchange.com/a/39552/6944 $\endgroup$ Commented 9 hours ago
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$\begingroup$ you have additional discussion here space.stackexchange.com/a/39588/12102 and here space.stackexchange.com/a/26628/12102 $\endgroup$– uhohCommented 3 hours ago