Simply unassign your chosen Keyword and assign it with the new campaign.
To do so, go to your Keyword List page:
1. Click on the action drop down menu for your chosen Keyword. Select Unassign.
2. Once unassigned, the same drop down menu will allow you to assign it to another campaign.
Once unassigned, you will not be able to access any data from that campaign, so make sure you don't need any of the Responses and Reports before doing so.