You can figure this out from first principles. Here's how:
First, you will need the critical angle for the acrylic material. This is the steepest angle that light can strike the acrylic/air interface and still be totally reflected, and it follows from the basic laws of refraction.
sin(t) = n1/n2
Where n1 and n2 are the refractive indices of the air and rod. Then, you have a geometry problem to work out how that fits in with the curve of the rod. Here's a diagram; the edges of the rod are black, the ray of light is red, the blue and green are constructions to help solve it.
The rod of diameter d is bent around a curve of radius r. The light beam is tangent to the inner edge at B, and strikes the outer edge at angle t - so it stays in, but only just. Angle OBA is between a radius and a tangent, so is a right angle.
We can then express t using some trigonometry as
sin(t) = r/(r+d)
Serendipity! we already know sin(t) in terms of refractive indices, so we can write:
n1/n2 = r/(r+d)
And re-arrange for r:
r = d/(n2/n1 -1)
If we use the refractive index of air (n1=1) and acrylic (n2=1.49) then this simplifies to
r > 2.04d
Now, there may be slight variations in refractive index for different acrylic grades, and for different wavelengths, so you'll probably want to keep to a bend radius a bit larger than that, but it should give a good starting point.