All Pew Research Center surveys about U.S. politics and policy include questions about partisan affiliation. In 2016, from January through August, a total of 8,113 registered voters were asked the following:

In politics TODAY, do you consider yourself a Republican, Democrat, or independent?

(IF INDEPENDENT, OTHER, DON’T KNOW): As of today do you lean more to the Republican Party or more to the Democratic Party? Detailed demographic
breakdowns of party identification are presented here, or can be downloaded (CSV or PDF).

Report:
The Parties on the Eve of the 2016 Election: Two Coalitions, Moving Further
Apart

Party ID among Hispanic voters