Mutations in LMNA, which encodes A-type lamins, result in disparate diseases, known collectively as laminopathies, that affect distinct tissues, including striated muscle and adipose tissue. Lamins provide structural support for the nucleus and sites of attachment for chromatin, and defects in these functions may contribute to disease pathogenesis. Recent studies suggest that A-type lamins may facilitate connections between the nucleus and the cytoskeleton mediated by nuclear envelope nesprin and SUN proteins. In mammalian cells, however, interfering with A-type lamins does not affect the localization of these proteins. Here, we used centrosome orientation in fibroblasts, which requires separate nuclear and centrosome positioning pathways, as a model system to understand how LMNA mutations affect nucleus-cytoskeletal connections. We find that LMNA mutations causing striated muscle diseases block actin-dependent nuclear movement, whereas most that affect adipose tissue inhibit microtubule-dependent centrosome positioning. Genetic deletion or transient depletion of A-type lamins also blocked nuclear movement, showing that mutations affecting muscle exhibit the null phenotype. Lack of A-type lamins, or expression of variants that cause striated muscle disease, did not affect assembly of nesprin-2G and SUN2 into transmembrane actin-associated nuclear (TAN) lines that attach the nucleus to retrogradely moving actin cables. Nesprin-2G TAN lines were less stable, however, and slipped over the nucleus rather than moving with it, indicating that they were not anchored. Nesprin-2G TAN lines also slipped in SUN2-depleted cells. Our results establish A-type lamins as anchors for nesprin-2G–SUN2 TAN lines to allow productive movement and proper positioning of the nucleus by actin.