Legally, as much as he likes. It’s a free country, it’s his property, and he doesn’t have to rent it out at all if he doesn’t want to.
Practically, there are limits. If he asks for more than the market permits, no one will rent from him. They will just find another similar place at a lower rent. But if the market is “tight” – not many vacancies – then every landlord is in a position to charge “what the market will bear” – that is, a lot.
There might be some legal restrictions on how much rent the landlord may charge, depending on where you live. Some communities have rent control laws. Some of these laws restrict how much the landlord may charge a new tenant coming in, but most allow him to charge whatever he likes to the new tenant and then restrict the amount by which he may raise the rent. These laws should be called “rent increase control” laws rather than “rent control” laws, but everyone calls them “rent control” laws.