Yes, the USCIS may grant you permission to take up employment in the U.S. on
To obtain Employment Authorization you will need to file Form I-765, application for employment authorization, with the USCIS Service Center which covers your place of residence in the U.S after your arrival there.
Note: The EAD can only be issued for the validity of the K-2 visa, 90 days. It is currently taking USCIS 90 days or longer to process the I-765
The documents required for K-2 visa are: