This is a question for which the answer depends on what you mean by “501(c)(3)” and by “on.”  Are you talking about a 501(c)(3) public charity, or a 501(c)(3) private foundation? Are you urging the donors to vote “on” a ballot question, without regard to how they should vote, or are you urging them to vote for (or against) the ballot question?

 As you know, the Tax Code prohibits a 501(c)(3) charity of any type from endorsing or opposing a candidate for public office at any level. (If the current efforts to repeal or narrow the so-called “Johnson Amendment” are successful to overcome the prohibition, this rule could change for charities generally, or perhaps only for churches and other types of 501(c)(3) religious organizations. (See Commentary: “Keep Charities Out of Politics”)) 

The Tax Code, however, permits a certain amount of lobbying on legislation. The IRS considers taking a position in favor of or in opposition to a public referendum, such as whether a state or local government should issue tax-exempt bonds for public improvements, to be a lobbying activity because the voters as a whole are the ultimate legislative decision makers. A public charity is permitted to lobby so long as it is not a substantial part of its activities. (See Ready Reference Page:  “Lobbying Rules Create Opportunities for Charities”) A private foundation may generally not engage in lobbying, although it may lobby in “self-defense” for or against proposed legislation that would affect its powers or responsibilities.

If your charity is just asking donors to vote, without suggesting how they should vote, a public charity could do it. A public charity could also suggest how the donors should vote so long as it is not a substantial part of the charity’s total activities. A private foundation would run a risk just getting involved in the question and could undoubtedly not suggest how the donors should vote.