You will need the Full Write Pledges permission to perform this action.
You can delete a pledge from any screen which lists them. See this article for all the places you can find pledge information.
Locate the pledge you want to delete in the table, click on the arrow in the dropdown at the end of the row and select "Delete". A confirmation message will appear. Click Yes to finish deleting the pledge.
Deleting a pledge will NOT delete any contributions credited to the pledge.