Does the buyer of raw cotton (who is a registered person) from the farmer need to pay GST on Reverse Charge basis?

Yes. As the cotton under heading 5201 and 5203 has been placed under 5% rate and the cotton farmer is not liable to registration, the buyers of raw cotton (who are registered persons) from the farmers are required to pay tax on reverse charge basis as per Section 9 (4) of the CGST Act, 2017.