RevolutionPlot3D
will distort the texture badly. Things will look much better if you use ParametricPlot3D
. Here is an example.
Animate[ParametricPlot3D[{Sin[t], Cos[t], u}, {t, 0, 2 Pi}, {u, -10, 0.02},
PlotStyle -> Texture[ExampleData[{"TestImage", "Lena"}]],
SphericalRegion -> True,
Mesh -> None,
Boxed -> False,
Axes -> None,
BoxRatios -> {1, 1, 2},
Lighting -> "Neutral",
ViewPoint -> {100 Cos[θ], 100 Sin[θ], -5}],
{θ, 4. π/3, 10. π/3, 2. π/12},
Deployed -> True,
DefaultDuration -> 30]

Note that the animation actually rotates the camera's position (the view point) around a fixed cylinder rather than rotating the cylinder while keeping the camera fixed. It is really easier to do this by rotating the camera.