By 6%, I'm assuming you're five generations removed from the Jew in question. We're 6.25% of one of our great-great-grandparents. I guess you discovered a family tree or other lore that labeled this twice-great grandparent as a Jew. If not, and and you're using a DNA test that suggests a certain percentage of Jewish ancestry, then the answer is no since Israel does not accept those in seeking citizenship under the Right of Return for Jews.
Here's the thing: The general rule is that you have to have on Jewish grandparent to make Aliyah (or gain citizenship as a Jew). This can be a bit tricky to define, since it also takes into account the general Jewish rule that one born to a Jewish mother is a Jew. If you're born to a Jewish father, then you'd need to convert. If your great-great-grandparent is female, and you're descendant of her daughter then you could theoretically make the argument. That daughter's child could be a Jew and thus you may be able to make Aliyah. One thing is that your paperwork would be heavily scrutinized, and you may have a hard time finding all the right documentation (birth certificates, wedding ketubas, gravestones, etc.) to prove to Israel than they should admit you under the Right of Return laws.
I'd say that it's unlikely that your great-great-grandparent was a woman and you're descendant through her daughter. That's a 1/4 chance alone, though I think at this time men were the ones most likely to marry out so that'll lower it further. Given how removed you are from the Jewish community, I'll assume someone converted out and that itself will probably disqualify you from taking advantage of the Right of Return, since it's for Jews and converting out nullifies that status (for them and any descendant born afterward). Even if they didn't, they weren't likely heavily involved with the Jewish community so it'll be hard to really show them as Jews.