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 ($zsim0.53$) 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 $0.47le zle 0.59$. We obtain a signal-to-noise ratio $S/Nsimeq 56$ 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 $S/Nsimeq 26$. These measurements form the basis of the halo occupation distribution and cosmology analysis presented in More et al. (Paper II).
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