Air Carrier Captain reported he mistakenly handled the Dangerous Goods Form by giving Captain's copy to ground personnel rather than keeping the Captain's copy on aircraft to destination.

Narrative

I was called out on Reserve at XX00 local for hot standby with a show time of XY30 local. On the drive to the airport I was assigned flight X to ZZZ with an XZ40 local departure on Date. The FO (First Officer) and I arrived at the aircraft approximately 50 minutes prior to departure. The plane was already loaded and both [Dangerous Goods Forms] were sitting on the Captain's seat. After taking our time to complete all of our required preflight prep; we were ready to leave at XZ20 local. I signed both [Dangerous Goods Forms] and saw the Ramp Supervisor in the cab of a tug at the bottom of the steps. In an effort to be helpful; I took both [Dangerous Goods Forms] down the steps and handed them to her. I came up the steps; shut the door; and we waited until we were XZ25 local to depart. Upon arriving in ZZZ; the Ramp Supervisor came upstairs and asked if the steps were positioned ok and then asked if we had a [Dangerous Goods Form]- as the envelope was empty. I stated that we should - there was approximately [lbs. of Hazardous Material] on board. I couldn't figure what happened to the [Dangerous Goods Form]. Then I realized that I had handed both copies out the door. I went and found the Ramp Supervisor and explained that I screwed it up and apologized. I have been a Captain for X weeks and have been very deliberate about not rushing and making sure everything is completed in accordance with the AOM and FOM. I have a mitigation plan for the [Dangerous Goods Form] that requires me to check if one is required and whether or not I've signed it. In this case; my plan did not trap this error. In retrospect; I should have called the Ramp and requested the Ramp Supervisor to retrieve the [Dangerous Goods Form]. I have never put a [Dangerous Goods Form] a DG envelope in 15 years. I am aware of this threat now and will not let it happen again.