What percentage of atheists claim to be a Democrat?

This is a difficult question to answer, because the data do not support a simple "Democrats are X and Republicans are Y" interpretation. There are some politicians who like to link "Atheism" and "Democrats" (usually this claim is linked with the claim that Republicans are much more religious and therefore better to vote for), but statistics show no firm correlation between political party and belief in a religion. In fact, there are atheists and agnostics in both parties.

But you probably would not know that, since the media tend to focus on extremes, and at this point in our politics, the extremely religious (usually members of conservative Christian denominations) are very dominant in the Republican party. This means the Republicans who espouse conservative Christian views get the majority of the interviews and since this view seems to attract the Republican base, numerous candidates who want to get elected make religiOSity an issue. But that does not mean that all Republicans are conservative Christians, nor does it mean that all Democrats are godless.

According to studies conducted by reputable demographers, about 14-20% (the numbers vary with the polls) of Americans identify as atheists, or as people with "no religion." Many are neither Republicans nor Democrats, preferring a libertarian candidate, or choosing candidates based on issues rather than on party. Some polls do say that a larger percentage of people with "no religion" vote for Democrats, but it is difficult to make a correlation, since a large number of people who are members of an organized religion also vote for Democrats. The Democrats as a party have members with a wide range of views, some of whom are indeed religious and others of whom are not religious at all. So, while it would thus be difficult to give a percentage of atheists who claim to be one party or the other, it is fair to say that, in our current political climate, Democrats are less dominated by conservative Christian viewpoints than Republicans are.