I don't think you can get it directly, but there are a few ways to find it indirectly.
One way is to use the GC.GetTotalMemory method to measure the amount of memory used before and after creating your object. This won't be perfect, but as long as you control the rest of the application you may get the information you are interested in.
Apart from that you can use a profiler to get the information or you could use the profiling api to get the information in code. But that won't be easy to use I think.
See Find out how much memory is being used by an object in C#? for a similar question.