That’s possible. Mail your return. The IRS will contact you to sort it out.
Someone else claimed my dependent and my return was rejected
If someone else claimed your dependent already, then your e-filed return will be rejected. Print, sign and mail your own return which claims your dependent. Mailed returns are processed differently by the IRS. It will take some time (maybe even up to a year) but eventually the IRS will contact both parties and sort out who could rightfully claim the dependent. The person who wrongfully claimed the dependent will face repayment of refund $, plus penalties.
When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s. Use a mailing service that will track it, such as UPS or certified mail so you will know the IRS/state received the return.