  Quantifying entanglement is an important task by which the resourcefulness of
a quantum state can be measured. Here, we develop a quantum algorithm that
tests for and quantifies the separability of a general bipartite state by using
the quantum steering effect, the latter initially discovered by Schr\"odinger.
Our separability test consists of a distributed quantum computation involving
two parties: a computationally limited client, who prepares a purification of
the state of interest, and a computationally unbounded server, who tries to
steer the reduced systems to a probabilistic ensemble of pure product states.
To design a practical algorithm, we replace the role of the server with a
combination of parameterized unitary circuits and classical optimization
techniques to perform the necessary computation. The result is a variational
quantum steering algorithm (VQSA), a modified separability test that is
implementable on quantum computers that are available today. We then simulate
our VQSA on noisy quantum simulators and find favorable convergence properties
on the examples tested. We also develop semidefinite programs, executable on
classical computers, that benchmark the results obtained from our VQSA. Thus,
our findings provide a meaningful connection between steering, entanglement,
quantum algorithms, and quantum computational complexity theory. They also
demonstrate the value of a parameterized mid-circuit measurement in a VQSA.
