What is a good enough putnam score to include in an application to PhD programs?
I think saying you were among the top "N" participants where N is something like 500, 200, 100, or less would be the right way to phrase the accomplishment.

The (anonymized) scores and rank of all participants are published, so you can find your exact rank.  Very roughly, I'd say top 50ish programs in math would view a top 500 rank favorably, top 20ish would like top 200, top 10 would like top 100, and the most elite would only view Putnam fellow or one of the (next "X") categories as noteworthy.  I think CS theory views math contest ability in a similar manner to pure math programs so that this mostly still applies.