Bring a large pot of salted water to a boil. Add pasta and cook, stirring occasionally, until al dente.
While pasta is cooking, heat oil in a large, straight-sided skillet over medium-high heat. Add garlic, anchovies, and raisins, and cook until fragrant, about 2 minutes. Stir in pine nuts.
Drain pasta, reserving 1/2 cup pasta water. Add pasta to the pan, and stir to combine. Moisten with pasta water as necessary. Stir in half the pecorino, and season with salt and pepper to taste.
Divide pasta between four plates, and top each with a dollop of ricotta, a handful of radicchio, and a sprinkling of the remaining pecorino.