Hi John

During the lysis or post lysis of cells expressing the recombinant protein, one can add a step for RNA removal by adding RNAse upto  5 to 10 microgram/ml followed by incubation with mild shaking for additional 30 minutes at room temperature. Since RNAse will not cleave DNA so it is specific for RNA removal. I hope it works for you 

If you want to remove all bound nucleic acids, not just RNA, include an anion exchange step in the purification.

Anion exchange makes sense but do you risk simply over loading the column? 

If this is a problem, the solution is just to use a bigger column (or a smaller sample). Ion exchange chromatography can be scaled up easily.

As Taran mentioned, the easiest method is to add some RNaseA. This will work in most cases but, if it doesn't, then Adam's suggestion of ion exchange chromatography tends to do the trick ... however, there are proteins that simply won't relinquish their bound RNA that easily.  I had problems removing RNA from my proteins using the aforementioned methods, which was hardly surprising as the proteins were viral nucleocapsid proteins whose main job is to bind and protect viral genomic single-stranded RNA from damage.

The method that eventually worked for me involves washing the sample with high ionic strength buffers (1 to 2 M NaCl or NaBr) during affinity and size exclusion chromatography. Here's a reference to how we managed to remove the RNA from Schmallenberg virus nucleocapsid protein.

Ariza et al., 2013, Nucleic Acids Research, 41 (11): 5912-46

One more thing, RNaseA will specifically remove RNA, whereas both ion exchange chromatography and high ionic strength washes will remove both RNA and DNA.

Also, if the nucleic acid is an intrinsic part of the folded protein, removing it can make the protein unstable and then potentially unfold and crash out of solution.