  We consistently couple simple continuum field theories with fracton
excitations to curved spacetime backgrounds. We consider homogeneous and
isotropic fracton field theories, with a conserved $U(1)$ charge and dipole
moment. Coupling to background fields allows us to consistently define a
stress-energy tensor for these theories and obtain the respective Ward
identities. Along the way, we find evidence for a mixed gauge-gravitational
anomaly in the symmetric tensor gauge theory which naturally couples to
conserved dipoles. Our results generalise to systems with arbitrarily higher
conserved moments, in particular, a conserved quadrupole moment.
