Yes, you can, but to sponsor your family as a freelancer, you will need a ministry of labor contract. This contract is required to mention a minimum monthly salary of AED 4,000. Simply put, if you want to sponsor your family, you will need to place a salary of 4000 or higher.
Afterwards, freelancers need to pay their monthly listed salary + VAT. Then, the salary amount will be transferred back to them to their bank accounts, through the WPS (Wage Protection System) every month.