Actually, Emac, the burden of proof lies with you. Advocating the killing of potential innocents with drones violates those innocents' rights to life and to a fair trial, which means you must provide some justification demonstrating that the use of drone strikes reduces terrorism. (That's if we're generous enough to grant the rather odious utilitarian calculus involved in deciding for others whether or not their imminent deprivation of life is 'worth' reducing terrorism. I don't grant it, but for sake of argument we'll set it aside.)
Your argument is that because terrorism existed before drone strikes, drone strikes can't cause terrorism. This argument is terrible. Death existed before guns and knives, but both of those can cause death.
Your other argument is that drone strikes are working because we have not suffered another terrorist attack on American soil. In the first place, this is explicitly false; see the 2013 Boston Marathon bombings. In the second place, your restriction of the location to American soil is without merit, and we can see ample terrorist attacks on Americans abroad (primarily but not entirely soldiers) since the use of drones, further demonstrating the argument is false. In the third place, even if your statement were true, correlation does not mean causation; again looking at your arbitrary and unmerited restriction to American soil, the logistics of launching a terrorist attack in the United States are sufficiently difficult to deter terrorists in the region where drone strikes are deployed. How do we know that fear of drone strikes, or death by drone strikes, has been the reason why the US has not suffered a terrorist attack (ignoring again the Boston Marathon incident)?