Yes, as an owner (in addition to mineral producers) of the mineral interest you are entitled to a depletion deduction of 15%. The IRS allows for a recovery for that depletion of a mineral resource.
In addition to the depletion, you are allowed deductions for taxes and other production costs based on the oil extraction. The drilling company typically shows these amount on your royalty statement. Royalties are reported in their gross amount, but you likely received an amount net of these costs so look over the statements carefully to deduct the differences.
Lastly, if you owned the property in addition to the mineral rights you could deduct the property taxes associated with the property (assuming its vacant land). Check with your state also. Some may offer additional depletion allowances and if they do, you would deduct under the state return.
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