You can only use the standard mileage rate if you own or lease the car.
https://www.irs.gov/taxtopics/tc510
Ownership is generally determined by the title, as governed by the laws of your state. If you were given the car to use, you can't deduct the mileage. If you were given the car to own, you need to get it re-titled and re-registered and re-insured in your name.
The standard mileage rate includes allowances for depreciation and insurance. You probably can't insure the car in your name if you don't own it, and you can't claim depreciation for property you don't own. You can use the exact expense method, if you have records. This means keeping a record of all car expenses you pay for the entire year, and a record of al business mileage. Then you deduct a percentage of provable expenses equal to the percentage of business use. Don't include any expenses you didn't pay yourself.
If you were given the car to own, and have been delayed in getting a new title, claiming the standard mileage method is technically illegal until you get the car titled in your name. If you are audited, a kind examiner might give you leeway if you show you made reasonable efforts to title and insure the car in your name but were delayed for reasons beyond your control, such as the pandemic. But that presumes a kind examiner. It will definitely be a major audit risk.
