Can a Non resident Indian open a LLC in Wyoming ?
Any person or legal entity can form an LLC in Wyoming.
As far as taxes go, after your LLC is formed you will need to obtain an EIN for it listing yourself as the responsible party (we can help you obtain EIN without Social Security Number).
Closer to the tax period your accountant will be able to help you obtain ITIN (personal tax ID) that you would use to pay taxes on your US income. If you are the only member of the LLC then your LLC taxes will be filed on the same tax return as your personal taxes (the LLC in that case is called "disregarded entity").