  We formulate and prove a local arithmetic Siegel--Weil formula for GSpin
Rapoport--Zink spaces, which is a precise identity between the arithmetic
intersection numbers of special cycles on GSpin Rapoport--Zink spaces and the
derivatives of local representation densities of quadratic forms. As a first
application, we prove a semi-global arithmetic Siegel--Weil formula as
conjectured by Kudla, which relates the arithmetic intersection numbers of
special cycles on GSpin Shimura varieties at a place of good reduction and the
central derivatives of nonsingular Fourier coefficients of incoherent Siegel
Eisenstein series.
