As an F1 student in the US, can I visit another University in the US for one term to carry out some research project with a professor there?
F1 regulations are quite strict and many conditions need to be followed there. So it may not be straightforward. You can always transfer to another university but then only a certain amount of credit may be transferred.
I would look in to the definition of "visit", as long as you are maintaining the required load and following regulations of your current university and department you are fine.