Yes and no. "501c3" is a tax designation granted by the IRS to qualifying non-profit entities. The most typical type of non-profit entity is a "Non-Profit Corporation," which is a specific type of entity that you can form in any state. Non-Profit Corporations can be granted 501c3 status by the IRS. The problem is that there is currently no such entity as a "Non-Profit LLC," and as such an LLC cannot itself obtain 501c3 status.
However, if you're dead set on having an LLC as part of a non-profit organization, there is a workaround if all of the following are true: (1) the LLC is owned 100% by a Non-Profit Corporation; (2) the LLC's managers are the same people who serve on the board of directors of the Non-Profit Corporation; and (3) the LLC Operating Agreement adheres to the bylaws and restrictions of its parent Non-Profit Corporation. If all of those requirements are met, then charitable donations to the LLC will be considered charitable donations to the Non-Profit Corporation and tax-deductible through the Non-Profit Corporation's 501c3 status.