People born in countries outside the United States but currently living here cannot, in most cases, vote in U.S. elections unless they’ve first been lawful permanent residents (with a green card) for some years then successfully applied for naturalized U.S. citizenship. This is frustrating for many who’ve applied for citizenship, because processing government delays currently stretch months and even years.
The clock is ticking for anyone wishing to vote in the next U.S. election, especially since many states require registration 30 days in advance. (It’s much less in some states, however, and can be done practically last minute in states like Colorado, Connecticut, New Hampshire, and Nevada).
Sadly, even if you’ve been approved for U.S. citizenship, you cannot call yourself a citizen until you’ve been sworn in. There is little you can do to hurry the process along, other than making sure to keep USCIS informed if you change your address, so as not to miss a notification.
One other possibility, though unlikely, is to see whether you have become a U.S. citizen automatically, either because you “derived” this status from U.S. citizen parents at your birth, or because you “acquired” it from parents who naturalized later. In some cases, citizenship can pass from grandparents to someone’s parents without the parents having realized it, and then pass in turn to the child. See U.S. Citizenship by Birth or Through Parents for more on this. You’d definitely want to consult an attorney, however, because the laws are complex and depend on the year of your birth, and obtaining proof that you’re a citizen (most likely a U.S. passport) could be tricky, especially when you’re in a hurry.
Whatever you do, don’t attempt to register or vote in a U.S. election unless you’re sure you’re eligible. Falsely claiming to be a U.S. citizen can make you deportable from the United States.