  We formulate the Lagrangian perturbation theory of galaxy intrinsic
alignments and compute the resulting auto and cross power spectra of galaxy
shapes, densities and matter to 1-loop order. Our model represents a consistent
effective-theory description of galaxy shape including the resummation of
long-wavelength displacements which damp baryon acoustic oscillations, and
includes one linear, three quadratic and two cubic dimensionless bias
coefficients at this order, along with counterterms and stochastic
contributions whose structure we derive. We compare this Lagrangian model
against the three-dimensional helicity spectra of halo shapes measured in
N-body simulations by Akitsu et al (2023) and find excellent agreement on
perturbative scales while testing a number of more restrictive bias
parametrizations. The calculations presented are immediately relevant to
analyses of both cosmic shear surveys and spectroscopic shape measurements, and
we make a fast FFTLog-based code spinosaurus publicly available with this
publication.
