We report a measurement of the ratio of the tt to Z/γ∗ production cross sections in √s=1.96  TeV pp¯ collisions using data corresponding to an integrated luminosity of up to 4.6  fb−1, collected by the CDF II detector. The tt cross section ratio is measured using two complementary methods, a b-jet tagging measurement and a topological approach. By multiplying the ratios by the well-known theoretical Z/γ∗→ll cross section predicted by the standard model, the extracted tt cross sections are effectively insensitive to the uncertainty on luminosity. A best linear unbiased estimate is used to combine both measurements with the result σtt¯=7.70±0.52  pb, for a top-quark mass of 172.5  GeV/c2.