A quick search brings up a few tests which suggest that voter reminders are effective at increasing turnout of the targeted groups. As J.C. points out in their answer, these attempts used existing tools like SMS message instead of a unique app, as people who go out of their way to download a special voting reminder app are almost certainly going to vote.
In a 2009 paper Don't Forget to Vote: Text Message Reminders as a Mobilization Tool, political scientists Allison Dale and Arron Strauss suggest that impersonal reminders (such as from a text message) are sufficient to create a statistically significant increase in voting rate:
Text messaging is examined as an example of an impersonal, noticeable communication to potential voters. A nationwide field experiment (n = 8,053) in the 2006 election finds that text message reminders produce a statistically significant 3.0 percentage point increase in the likelihood of voting. While increasing social connectedness has been shown to positively affect voter turnout, the results of this study, in combination with empirical evidence from prior studies, suggest that connectedness is not a necessary condition for a successful mobilization campaign. For certain voters, a noticeable reminder is sufficient to drive them to the polls.
Note: I don't have access to the full text, so my conclusions here are from the Abstract alone
Vote.org is "the largest 501(c)(3) non-profit, non-partisan voting registration and get out the vote (GOTV) technology platform in America". They carried out studies evaluating their effectiveness:
Over the past two years, we have run a number of large-scale controlled experiments in partnership with the Analyst Institute, Pantheon Analytics, and the Harvard Kennedy School of Government. Read more below
For the 2018 general election, Vote.org conducted SMS voter mobilization programs covering 12,681,951 people of color and unmarried women in 33 states. These programs used “cold” text messaging to registered voters who have no prior relationship to Vote.org
Vote.org’s SMS treatments increased turnout in the 2018 election, generating an average increase in turnout of 0.26 percentage points at a cost per net vote of $85.69 (11.7 net votes/$1000).
The program caused 17,586 people to vote who otherwise would have missed participating in the 2018 General Election.
Vote.org’s SMS messages increased voter turnout among people who had requested a ballot. On average, the treatments generated a 0.21 percentage point increase in turnout at a cost per net vote of $75.14 (13.3 net votes/$1000).