The rabbinate is actually doing its best to not impose at all. There are many tithes separated from produce in Israel and the rabbinate, in certifying that given produce is kosher (if requested to do so by the grower), only removes those tithes which cannot be eaten nowadays, namely, Terumah Gedolah and Terumat Maaser (totaling about 1% of the crop), plus in years 1,2,4,5 of the Shemitta cycle, there is 10% of the crop (called Maaser Sheni) whose value is redeemed onto a small coin before becoming edible.
There remains 10% of the crop (called Maaser Rishon) which should ideally be given to a Levi, and, in years 3 and 6 of the Shemitta cycle, there is 10% of the crop (called Maaser Ani) which must be given to the poor. The rabbinate does not enforce this and many growers regularly, unfortunately, steal this from the poor. There is no holiness attached to that produce, so the food in the market is still Kosher to eat.
So to answer your question: yes there are tithes that need to be given to the poor, but the rabbinate generally does not impose this and it usually ends up getting stolen back by the grower :(