You can, if you want. If you generally agree with the DNC, labeling yourself a Democrat is a useful label to quickly get your views across. You wouldn’t be a Leftist, since the goals and views of the DNC are a maintaining of the Capitalist status quo, but you would be a Liberal, if you want a non-party label to use instead.
I do think familiarizing yourself with Leftist theory would help you make sense of where Leftists are coming from.