Kaon production in one prong tau decays has been studied using data collected with the DELPHI detector at the LEP collider. Charged kaons were identified over a large momentum range by the DELPHI barrel Ring Imaging Cherenkov detector. The following branching ratios have been determined: BR(tau --> Knu(T)) = (0.85 +/- 0.18) %, BR(tau --> Knu(tau) greater-than-or-equal-to 0 neutrals) = (1.54 +/- 0.24) %, BR(tau --> Knu(tau) greater-than-or-equal-to 1 neutrals) = (0.69 +/- 0.25) %. The result for the exclusive branching ratio is consistent with the Standard Model prediction based on tau - mu - e universality. In addition, tau decay into K*- was studied in the channel K*- --> K- pi0. The result BR(tau --> K*-nu(tau)) x BR(K*- --> K- pi0) = (0.57 +/- 0.23)% was obtained.