As a layman, I have always been fascinated by magnetism, gravity, and angular momentum.
Where does AM fit in physics? Is it fully understood or are the mysteries? Does it effect space-time at all. Does a fast spinning star warp space-time more or less than a star of the same mass spinning slower? Would a clock on the outer edge of a fast spinning top keep different time than a clock in the center of the same top? Is it possible that matter is just energy trapped in some a gyroscopic state? What happens to a magnetic field that is spun at super high speed?
I'm not a layman, but I'm still fascinated by 'motion'. Why do things move? what is 'force'? Well, that's another story, another thread.
I'm surprised no one has attempted to answer your question which I think is important. I'll try what I know, some experts in mechanics or atomic physics can always step in and educate me also.
If a mass warps space-time, then angular momentum must have some effect on warping. In physics angular momentum is defined as I*w ( I times omega) or (moment of Inertia, 'I')*(angular velocity, w).
But the interesting thing is 'I' (moment of inertia, some books also use the term 'rotational inertia') depends on the mass of the object. In fact in some places of physics 'mass' can be replaced with 'rotational inertia' when motion is circular as opposed to linear. One example comes to my mind is kinetic energy, for linear motion it is (1/2)mv^2, and for rotational motion it is (1/2)Iw^2. Here v is linear veolicty, w is angular velocity. But note that mass m is replaced by I, rotational inertia.
If mass and rotational inertia are in some way equivalent , I can see why angular momentum can also have effect on space-time warping. But I do not know exactly how much and in what way.
The intersting thing about angular momentum is its conservation property, total angular momentum of a system must remain the same after the system undergoes a change. That is also the property astronomers use to explain spinning and mass of a distant stars. If a star shrinks but mass remains the same, its spinning speed will increase, because its angular momentum must remain the same as before it started shrinking. By shrinking star's 'I' gets lower, therefore speed 'w' must go higher.
So, my final comment is , yes, I see an effect of angular momentum on warping of space time, if we go Einstein's way.