  The topological $\theta$-angle in gauge theories engenders a series of
fundamental phenomena, including violations of charge-parity (CP) symmetry,
dynamical topological transitions, and confinement--deconfinement transitions.
At the same time, it poses major challenges for theoretical studies, as it
implies a sign problem in numerical simulations. Analog quantum simulators open
the promising prospect of treating quantum many-body systems with such
topological terms, but, contrary to their digital counterparts, they have not
yet demonstrated the capacity to control the $\theta$-angle. Here, we
demonstrate how a tunable topological $\theta$-term can be added to a prototype
theory with $\mathrm{U}(1)$ gauge symmetry, a discretized version of quantum
electrodynamics in one spatial dimension. As we show, the model can be realized
experimentally in a single-species Bose--Hubbard model in an optical
superlattice with three different spatial periods, thus requiring only standard
experimental resources. Through numerical calculations obtained from the
time-dependent density matrix renormalization group method and exact
diagonalization, we benchmark the model system, and illustrate how salient
effects due to the $\theta$-term can be observed. These include charge
confinement, the weakening of quantum many-body scarring, as well as the
disappearance of Coleman's phase transition due to explicit breaking of CP
symmetry. This work opens the door towards studying the rich physics of
topological gauge-theory terms in large-scale cold-atom quantum simulators.
