  The color of a star is a critical feature to reflect its physical property
such as the temperature. The color index is usually obtained via absolute
photometry, which is demanding for weather conditions and instruments. In this
work, we present an astrometric method to measure the catalog-matched color
index of an object based on the effect of differential color refraction (DCR).
Specifically, we can observe an object using only one filter or alternately
using two different filters. Through the difference of the DCR effect compared
with reference stars, the catalog-matched color index of an object can be
conveniently derived. Hence, we can perform DCR calibration and obtain its
accurate and precise positions even if observed with Null filter during a large
range of zenith distances, by which the limiting magnitude and observational
efficiency of the telescope can be significantly improved. This method takes
advantage of the DCR effect and builds a link between astrometry and
photometry. In practice, we measure the color indices and positions of Himalia
(the sixth satellite of Jupiter) using 857 CCD frames over 8 nights by two
telescopes. Totally, the mean color index BP-RP (Gaia photometric system) of
Himalia is 0.750 \pm 0.004 magnitude. Through the rotational phased color index
analysis, we find two places with their color indices exceeding the mean \pm 3
\sigma.
