Is it legal for a business to require employees to use a personal social media for business use?

I would not have thought that any company or corporation could legally demand that an employee use an IT or computer system that they themselves have not provided. I also do not see how they could police what you you describe. Further I do not think that the directors of a business would wish to expose themselves to the dangers of running part of the business on systems over which they had no actual control. How would they deal with an employee they wished to dismiss - they could not stop that person's use of external social media to the detriment of the company.

I would suggest you sit down with your business' IT director and ask him/her to explain what they want, it may be that yo have misheard something.