The rise of social media has opened countless opportunities to explore social science questions with new data and methods. However, research on socioeconomic inequality remains constrained by limited individual-level socioeconomic status (SES) measures in digital trace data. Following Bourdieu, we argue that the commercial and entertainment accounts Twitter users follow reflect their economic and cultural capital. Adapting a political science method for inferring political ideology, we use correspondence analysis to estimate the SES of 3,482,652 Twitter users who follow the accounts of 339 brands in the United States. We validate our estimates with data from the Facebook Marketing API, self-reported job titles on users' Twitter profiles, and a small survey sample. The results show reasonable correlations with the standard proxies for SES, alongside much weaker or non-significant correlations with other demographic variables. The proposed method opens new opportunities for innovative social research on inequality on Twitter and similar online platforms.