This analysis suggests that any relationship between political affiliation and charitable donation isn't very strong. For what it's worth, the sign of the coefficient in the regression suggests that lefties give more than righties. (The paper also looks at volunteering, and finds that lefties volunteer quite a lot more than righties.)

I wouldn't make any large bets on the basis of that paper, though. There are lots of interrelated things here -- politics, wealth, religion, etc., etc., etc. -- and even if those regression coefficients indicate something real rather than just noise it may be much more complicated than "group X is more generous with their time/money than group Y". And it looks like it's the work of a single inexperienced researcher, and doesn't seem to be a peer-reviewed publication.

This paper -- not available for free, but there's an informal writeup by someone else here says that other research has indicated that righties give more than lefties (contrary to what the paper above says), and purports to explain this by saying that righties are more religious and the religious give more. More precisely, it looks as if religion leads to giving in two ways. There's giving to religious charities, which obviously religious people do a lot more of than irreligious ones; and there's other giving, which church attenders do and so (to a comparable extent) do people involved in other sorts of socially-conscious meeting up. ("Local civic or educational meetings" is the thing they actually looked at.)

If you control for religion, then allegedly the left/right differences largely go away.

Make of all that what you will. (What I make of it is: it's complicated.)