You can claim the home office deduction whether you rent or own your home.
There are two options. You can use a simplified option which is the square footage of the office times $5. If you use the regular method, part of the rent you pay may quality.
If you are self-employed, you can claim the deduction on Schedule C as part of the P&L for your business.
If you are an employee, you can claim the deduction on Schedule A if you itemize your deductions.