Can I bring portable closet from India to USA?

Nothing to stop you taking your closet as long as it fits in a suitcase or box which fits within the size and weight limits of the airline.

But unless it is a special design or a piece of furniture that has a high personal value, I would not bother. Better take those things you can not buy where you go and do not pay for extra luggage, (but that is my view rather than fact.)
Buying a new closet or having your current one send to you will likely be cheaper for a long stay, and for a short stay you can likely do without the closet or buy a cheap alternative (maybe second hand.)

Based on the comments a warning: Having that many steel tubes in your luggage may mean that it will be checked extra. Often that is by opening the case and having a look, likely with a dog trained to smell explosives near. It can also 'just' be a different scanner and an electronic device to check for explosives.