  The Dirac spin liquid (DSL) is a two-dimensional (2D) fractionalized Mott
insulator featuring massless Dirac spinon excitations coupled to a compact
$U(1)$ gauge field, which allows for flux-tunneling instanton events described
by magnetic monopoles in (2+1)D Euclidean spacetime. The state-operator
correspondence of conformal field theory has been used recently to define
associated monopole operators and determine their quantum numbers, which encode
the microscopic symmetries of conventional ordered phases proximate to the DSL.
In this work, we utilize semiclassical instanton methods not relying on
conformal invariance to construct monopole operators directly in (2+1)D
spacetime as instanton-induced 't Hooft vertices, i.e.,
fermion-number-violating effective interactions originating from zero modes of
the Euclidean Dirac operator in an instanton background. In the presence of a
flavor-adjoint fermion mass, resummation of the instanton gas is shown to
select the correct monopole to be proliferated, in accordance with predictions
of the state-operator correspondence. We also show that our instanton-based
approach is able to determine monopole quantum numbers on bipartite lattices.
