Yes, of course it will move. Here is a familiar science demonstration, the
mercury 'beating heart' BEATING HEART which
shows a crude battery circuit (the mercury and the iron in a
mild acid). When the iron touches the mercury, the battery
puts a current through the contact point, and that current
deforms the mercury because it creates a changing magnetic field.
The deformation breaks the contact, and the force on the mercury
goes away, which reestablishes electric contact... and it oscillates.
It's literally a changing magnetic field that's moving the mercury,
but the coil-in-a-field causes more of a torque effect than
a translational motion. The application of torque to a liquid
is a difficult thing to demonstrate; how would one know that
a liquid drop was rotating?
A drop of conductive liquid in a changing magnetic field WILL transformer-couple
to that field, and generate a little loop of internal current.
The problem, then, is to see a drop become nonspherical when
a changing magnetic field excites it, and then see some indication
of axial tilt due to a nonchanging magnetic field.
Probably, this could be accomplished, with stop-action video
to record droplets in free fall. It'll look like a bunch
of wires with a quivering raindrop falling through a magnet gap...