  A joint analysis of the clustering of galaxies and their weak gravitational
lensing signal is well-suited to simultaneously constrain the galaxy-halo
connection as well as the cosmological parameters by breaking the degeneracy
between galaxy bias and the amplitude of clustering signal. In a series of two
papers, we perform such an analysis at the highest redshift ($z\sim0.53$) in
the literature using CMASS galaxies in the Sloan Digital Sky Survey-III Baryon
Oscillation Spectroscopic Survey Eleventh Data Release (SDSS-III/BOSS DR11)
catalog spanning 8300~deg$^2$. In this paper, we present details of the
clustering and weak lensing measurements of these galaxies. We define a
subsample of 400,916 CMASS galaxies based on their redshifts and stellar mass
estimates so that the galaxies constitute an approximately volume-limited and
similar population over the redshift range $0.47\le z\le 0.59$. We obtain a
signal-to-noise ratio $S/N\simeq 56$ for the galaxy clustering measurement. We
also explore the redshift and stellar mass dependence of the clustering signal.
For the weak lensing measurement, we use existing deeper imaging data from the
CFHTLS with publicly available shape and photometric redshift catalogs from
CFHTLenS, but only in a 105~deg$^2$ area which overlaps with BOSS. This
restricts the lensing measurement to only 5,084 CMASS galaxies. After careful
systematic tests, we find a highly significant detection of the CMASS weak
lensing signal, with total $S/N\simeq 26$. These measurements form the basis of
the halo occupation distribution and cosmology analysis presented in More et
al. (Paper II).
