Form a technical perspective, you can. But it's hard to imagine why you would want to do that. A Trucker antenna will provide the same signal improvement when mounted on a structure as when mounted on a vehicle.
However, we recommend a Yagi, or directional, antenna for most fixed-site installations. A Yagi antenna provides more gain, or signal enhancement, to better compensate for signal lost due to the length of the connecting cable.
One other factor to consider: The FCC and Industry Canada both now require that all cell phone signal boosters be sold as kits with appropriate antennas included. Unless you were trying to cobble together a booster system from older, miscellaneous parts, there would be no reason to use a Trucker antenna on a building.