Yes, you can. In fact, most borrowers do not need a cosigner. They qualify for a loan based on a combination of a steady, sufficient income, good enough credit, and/or a substantial downpayment for the car being purchased. Since lenders assess the risk of a borrower failing to pay back the loan, someone who demonstrates an ability and a history of paying back their debt is usually approved.
If you have little or no credit history, or if you have had problems repaying money in the past, your options are fewer and more expensive without a cosigner, but they are out there. There are many reputable online lenders that specialize in providing loans for people who might not meet stricter bank or credit union criteria for approval.
Just be sure to check out your lender before applying to avoid any scams and hidden difficulties. Google the name of the lender and see if there are any complaints, reviews, or news coverage in which they are mentioned. Better to save yourself that headache.