  Coherence time and gate fidelities in Rydberg atom quantum simulators and
computers are fundamentally limited by the Rydberg state lifetime. Circular
Rydberg states are highly promising candidates to overcome this limitation by
orders of magnitude, as they can be effectively protected from decay due to
their maximum angular momentum. We report the first realization of
alkaline-earth circular Rydberg atoms trapped in optical tweezers, which
provide unique and novel control possibilities due to the optically active
ionic core. Specifically, we demonstrate creation of very high-$n$ ($n=79$)
circular states of $^{88}$Sr. We measure lifetimes as long as 2.55 ms at room
temperature, which are achieved via cavity-assisted suppression of black-body
radiation. We show coherent control of a microwave qubit encoded in circular
states of nearby manifolds, and characterize the qubit coherence time via
Ramsey and spin-echo spectroscopy. Finally, circular state tweezer trapping
exploiting the Sr$^+$ core polarizability is quantified via measurements of the
trap-induced light shift on the qubit. Our work opens routes for quantum
simulations with circular Rydberg states of divalent atoms, exploiting the
emergent toolbox associated with the optically active core ion.
