Is it legal for a company to make you cover your tattoos?

Yes, it is completely legal. Companies have the right to pass dress codes--and "dress" includes codes or rules for hair dye, for body art, for piercings, etc. Companies can require employees to dress in a way that they believe is professional, reflects their corporate culture, and/or is what their customers expect. The only dress which companies generally can't interefere with are  items of clothing, hair styles, etc. with religous significance--like a Muslim woman's covering, a Jew's yalmuke, or a Sikh's turban--though even there, if the clothing, hair, etc. poses safety issues, the company can restrict them.