  In this paper, the classical and quantum theory of $\mathcal{N}=1$
supergravity in four spacetime dimensions will be studied in the framework of
loop quantum gravity. We discuss the canonical analysis of the supergravity
Holst action as first introduced by Tsuda. In this way, we also derive a
compact expression of the supersymmetry constraint, which plays a crucial role
in canonical supergravity theories, akin to the role of the Hamiltonian
constraint in non-supersymmetric generally covariant theories. The resulting
theory is then quantized using loop quantum gravity methods. In particular, we
propose and discuss a quantization of the supersymmetry constraint and derive
explicit expressions of the action of the resulting operator. This is important
as it is the first step on the way of analyzing the Dirac algebra generated by
supersymmetry and Hamiltonian constraint in the quantum theory and for finding
physical states. We also discuss some qualitative properties of such solutions
of the SUSY constraint.
