You can use the exact method but you can't use the standard mileage method. The standard mileage method includes an allowance for depreciation, and you can't claim depreciation if you don't own the car.
For the exact method, you must keep track of all the car expenses for the entire year. Gas, oil changes, tires, repairs, maintenance, insurance, whether paid by you or your sister. You can't include depreciation as an expense. You can include interest included in the car payment but not the principle, and only if you pay the car payment. You must also keep track of the mileage driven for work, and the total mileage for the whole year (start and end odometer). You figure the percentage of business use by miles driven. You can then deduct either, the percent of car costs allocated to the percent of work miles, or the actual costs you paid, whichever is less.
(You can't claim, a deduction for tires, oil changes, and insurance unless you actually paid it. If your sister paid those expenses you can't deduct them.)
Also note, if your sister's insurance company finds out about this arrangement, they will probably cancel her policy, unless she has informed them of your use for rideshare and they increased her premiums to cover the risk. Your use of the car for rideshare may also violate the terms of the car loan, which might allow the lender to cancel the loan and demand immediate repayment or repossess the car. Be careful.
