How can I rotate a whole model by scripting?

Rotate about what? Rotation is an operation around a particular point. We can use GetModelCFrame as the default, but you could substitute whatever CFrame you wanted.

Secondly, in what way are you rotating it? Rotating around a single axis will work exactly how you'd expect, so that would be the easiest thing.

There's a few ways to accomplish the math, but here's the way that I like to think about it, because it makes the most sense in my head:

function rotate(cframe,about,x,y,z)
    local within = about:toObjectSpace(cframe);
    local out = about * CFrame.Angles(x,y,z);
    return out:toWorldSpace(within);
end

We would then use rotate on each part's CFrame in the model that we want to rotate about about (which could be the model's CFrame gotten through GetModelCFrame, or any other point, if you have one in particular you want). If we wanted to spin it 90 degrees around the vertical axis, we could give x,y,z the parameters 0,math.pi/2,0.