No site themselves will just give you something for nothing, but there are some websites that will start you with a free bankroll, I know some people who have done this, but there are strings. They take all of your rakeback, which for some people is an absolute no-no. They also make it that you can't cash that out until you have hit a certain amount of raked hands(namely enough raked hands to cover the amount that they gave you for your starting bankroll. You could probably search Google for "Free bankroll" and find some sites, but I would do my research and find out what they require you to do before the account is fully yours.
I know this has nothing to do with website bonus's, but this is all I can think of for what you are asking.