Does curvature of spacetime depend upon the "mass" or "density" of a object? Suppose we have a object with mass "M" with small density and a object with same mass "M" but different density (like a large density). Does the curvature of spacetime same for the two object with same mass but different densities?
 A: To start with, as pointed out in the comments,  your question is not very precise. I will assume you are referring to spherically symmetric bodies. Then Birkhoff's theorem implies that the exterior is described by the Schwarzschild solution, so as long as we are in the exterior of both objects they are indeed equivalent. The interior will depend not only on the density but also on the internal flux of energy-momentum. There are several different known solutions that may describe the interior of a Schwarzschild star, at least according to general relativity, so spherical symmetry does not in any way imply interior equivalence. I can provide some links at a later time if you wish, otherwise I believe it is relatively easy to find for yourself. 
A: 
I am not assume it spherical body,it may be any shaped object. My question is that Is curvature of spaectime proportional to mass or density

Look at the map below, it could be any shape, in this case it's a lumpy earth, not a perfect sphere. The bottom lines tells you where variations in density have affected the acceleration due to gravity.

So up close, on the ground, you are right, density variations do cause very very small distortions in  curvatures of spacetime compared to a completely regular sphere. But if you moved  to the distance of the moon, they would be so small that spacetime would be curved as if all the mass was at one point.
Now look at the asteroid Ida, which has a moon going around it, but it is just a lump of odd shaped rock.

That moon Dactyl is still following the curvature of spacetime produced by Ida, as if Ida was a point mass, but it's orbit will change over time, in all sorts of directions, because of the density variations of Ida. Our moon won't,  it will just slow down,  it's so far away from Earth
So the spacetime curvature produced by an object and felt by you, depend on it's mass, it's density variations and the distance you are away from it.
