Yes, non-residents can obtain a library card. The fee to obtain a library card for non-residents is different depending on the county you are applying in. In Sussex and Kent counties, the fee for non-residents is $25, and in New Castle county the fee is $40. You will still need to fill out the application and bring it to any local branch, along with the fee and a photo ID.
If you are a non-resident but own property in Delaware, you are eligible to receive a Delaware library card.