Are there any datasets for protectionism? Are there any data sources or variables that measure how protectionist a country is? If so, what are they?
Looked a bit further, I think I possibly found what you're looking for:

The Overall Trade Restrictiveness Index (OTRI) summarizes the trade policy stance of a country by calculating the uniform tariff that will keep its overall imports at the current level when the country in fact has different tariffs for different goods.

The data:
http://siteresources.worldbank.org/INTRES/Resources/469232-1107449512766/OTRI2009.xlsx

Background: http://econ.worldbank.org/WBSITE/EXTERNAL/EXTDEC/EXTRESEARCH/0,,contentMDK:22574446~pagePK:64214825~piPK:64214943~theSitePK:469382,00.html

hope this helps,
best regards