  We study two-dimensional celestial conformal field theory describing
four-dimensional ${\cal N}=1$ supergravity/Yang-Mills systems and show that the
underlying symmetry is a supersymmetric generalization of BMS symmetry. We
construct fermionic conformal primary wave functions and show how they are
related via supersymmetry to their bosonic partners. We use soft and collinear
theorems of supersymmetric Einstein-Yang-Mills theory to derive the OPEs of the
operators associated to massless particles. The bosonic and fermionic soft
theorems are shown to form a sequence under supersymmetric Ward identities. In
analogy with the energy momentum tensor, the supercurrents are shadow
transforms of soft gravitino operators and generate an infinite-dimensional
supersymmetry algebra. The algebra of $\mathfrak{sbms}_4$ generators agrees
with the expectations based on earlier work on the asymptotic symmetry group of
supergravity. We also show that the supertranslation operator can be written as
a product of holomorphic and anti-holomorphic supercurrents.
