We present new optical (BVI) time-series data for the evolved variable stars in the Carina dwarf spheroidal galaxy. The quality of the data and the observing strategy allowed us to identify 14 new variable stars. Eight out of the 14 are RR Lyrae (RRL) stars, four are Anomalous Cepheids (ACs) and two are geometrical variables. Comparison of the period distribution for the entire sample of RRLs with similar distributions in nearby dSphs and in the Large Magellanic Cloud indicates that the old stellar populations in these systems share similar properties. This finding is also supported by the RRL distribution in the Bailey diagram. On the other hand, the period distribution and the Bailey diagram of ACs display significant differences among the above stellar systems. This evidence suggests that the properties of intermediate-age stellar populations might be affected both by environmental effects and structural parameters. We use the BV Period--Wesenheit (PW) relation of RRLs together with evolutionary prescriptions and find a true distance modulus of 20.09+/-0.07(intrinsic)+/-0.1(statistical) mag that agrees quite well with similar estimates available in the literature. We identified four peculiar variables. Taking into account their position in the Bailey diagram and in the BV PW relation, two of them (V14, V149) appear to be candidate ACs, while two (V158, V182) might be peculiar RRLs. In particular, the variable V158 has a period and a V-band amplitude very similar to the low-mass RRL ---RRLR-02792---recently identified by Pietrzynski at al. (2012) in the Galactic bulge. ; Comment: Accepted for publication in ApJ, publication date September 20, 2013. 31 pages, 7 figure, 3 tables. Figs. 3 and 4 corrected, references added, minor corrections