I need to estimate potential voters in each Voting District by ancestry.
To convert any official geography to any other, consider http://mcdc.missouri.edu/websas/geocorr12.html.
One issue with linking recent PUMS data with voter districts is that the smallest available geography for recent ACS samples is the PUMA. Because PUMAs are dependent on population size, in most places a single PUMA will contain many voting districts. Furthermore many of the Voter District boundaries do not perfectly align with PUMA boundaries so it will be impossible to know a household falls in one voter district versus another if the boundaries overlap. The MABLE/geocorr tool suggested by skolenik is an excellent resource and would be a great way to determine which voting districts fall within each PUMA if you decide to go that route.
Another option, if aggregate data is acceptable for your research, would be to see if the information you are looking for is available through NHGIS. NHGIS is primarily focused on mapping data from Census produced summary files, but the extract engine can also produce readable .csv files with optional descriptive headers. A quick look at the available data shows that Ancestry information is not available at the voting district level, but it is available at the Congressional District and State Legislative District levels, which may match up better with the voting district boundaries. You can see what other geographic levels are available for the information you are interested in using the NHGIS data finder. A video introduction to the data finder is available on the NHGIS homepage, and their FAQ and User’s Guide areas are very informative.
I hope this helps.