To my knowledge, there is no such function for texture references, which is what you seem to be using right now. The analogy to a texture reference is a plain old C-style array, which is referenced by a pointer that gets passed around. If some code also needs the array dimensions, the size information needs to be passed separately.
A modern and somewhat more flexible alternative to classical texture references are texture objects. These are worth looking into, but I don’t know whether they are useful for graphics interop (my hunch is: no). For those, one can use cudaGetTextureObjectResourceDesc() to retrieve relevant size information.
I assume there is an equivalent driver API function, but I don’t know that.