A catalog of over ten million variable source candidates in ZTF data release 1

Variable sources probe a wide range of astrophysical phenomena. We present a catalog of over ten million variable source candidates found in Data Release 1 (DR1) of the Zwicky Transient Facility (ZTF). We perform a periodicity search up to a frequency of 160 day^-1, and we classify the light curves into erratic and smooth variables. We also present variability indicators and the results of a periodicity search, up to a frequency of 5 day^-1, for about 1 billion sources in the ZTF-DR1 light curve database. We present several new short-period (<90 min) candidates, and about 60 new dwarf nova candidates, including two candidate eclipsing systems. Both the 10 million variables catalog and ~1 billion source catalog are available online in catsHTM format.