It depends.
If you feel bound by halakhah (traditional Jewish law), then your answer, as my Orthodox and Conservative colleagues have stated, is clearly “no.”
But if your Jewish identity is not defined by or bound to observance of halakhah, traditional Jewish law, then it might well be “yes.” From a non-halakhic Jewish perspective, your answer might again depend on how you understand concepts like “work,” “rest,” and “holy.” It might further depend on how you experience God, and ultimately on how you choose to respond to the Jewish imperative to observe and remember Shabbat.
Shabbat is traditionally a day when all work is forbidden. It is a day of rest, a day to connect with God, Torah, Israel; a day to reset our spiritual compass to our truest and highest values. Most importantly, Shabbat is defined as kadosh, holy, something special, precious, set apart. Traditionally we observe Shabbat on the seventh day of the week because God observed Shabbat on the seventh day of creation, and we, created in God’s image, yearn to be like God. In Tanakh, the Hebrew bible, God defined Shabbat as holy, and so should we. God ceased from the work of creation, of world-building, and so should we.
So, what is voting to you, and in particular what is this specific vote, the one that coincides with Shabbat, to you?
Is it work, a secular act, part of the mundane world, a brick in the building that defines your every day existence and that separates you from holiness? Does voting separate you from the priorities that transcend quotidian tasks? Notwithstanding these very tasks keep us in the living, breathing state of being that allows us to bring those priorities to bear on this world God created, Shabbat is not for this.
Or is voting a sacred privilege, a sanctifying act, one that protects against the tyranny of material power, brings you face-to-face with your values and ideals? Does voting embody some of those ideals and help you to transcend, for a moment, the ordinary strivings of your daily, secular existence, plugging you into the vision of a just and peaceful world, a world where we may more regularly enjoy the respite and wholeness that Shabbat is meant to bring?
You might also (or instead) give this question the gut-test. Does voting on Shabbat enhance or impede your experience of Shabbat rest and holiness?
And yes, I am aware that I have answered a question with a question. What did you expect?
I hope you’ll let us know what path you choose.