A couple of the answers here are accurate but incomplete, so I want to add more weight to 5jj's reply since it best explains the writer's choice of stacked vs other verbs they could have used. Stacked is not only telling us that the conservatives have a big majority and not only that that the court has been filled (a neutral verb) with conservatives by past Presidents, but it's also giving us a hint about how the author feels about the situation. They probably don't like it and/or think it's unfair.
One of the definitions of packed, an alternative that probus offered, is "to influence the composition of so as to bring about a desired result." That carries a lot of the same meaning as stacked (and "packing the court" is also an idiomatic phrase), but stacked goes further with the connotation that the court-packing was unfair (and in other contexts it could also have the meaning that the stacking was done in secret, as 5jj pointed out).