Following discovery of the free radical SiCN in the C-star envelope IRC+10216, we report the detection in the same source of its isomer SiNC. The microwave spectra of SiNC and SiCN were studied in the laboratory and their rotational transition frequencies are accurately known. The ground fine structure state of SiNC, 2Π1/2, gives rise to a series of rotational transitions, spaced by 12.8 GHz, each with Λ-doubling. Five weak lines are detected with the IRAM 30-m telescope at the frequencies of the J=6.5 -> 5.5 (e), 7.5 -> 6.5 (f), 8.5-> 7.5 (f) and 10.5-> 9.5 (e) and (f) rotational transitions. Other SiNC lines from these or adjacent rotational transitions are found to be blended with stronger lines from known molecules. The lines assigned to SiNC have a cusped shape, characteristic of species confined to a hollow shell in the outer circumstellar envelope. They are twice weaker than their SiCN counterparts, which have the same shape, and presumably arise in the same region of the envelope. SiNC and SiCN have about the same abundance in IRC+10216, ̃4 × 10-9 with respect to H2. This contrasts with HCN, HC3N and HC5N, for which the cyanide to isocyanide abundance ratio is >100.