Not as a national price, and it is worth knowing why before you drive over on a Tuesday. Sonic's store-level pricing carries one price per item per location. There is no weekday column in it, for any item, at any of the 3,357 drive-ins in the data.
That does not make the specials people remember imaginary. Sonic drive-ins are independently owned and run their own promotions, and the app pushes offers that change week to week and differ by account. Both are real. Neither is something a national price guide can quote you, and any page printing a Tuesday burger price is quoting one store or quoting nothing.
The one genuinely everyday exception is Happy Hour, and it is everyday in the literal sense: 2 to 4 PM on all seven days rather than on a particular one. That makes it the closest thing Sonic has to a daily special, and the only one that needs no app and no code.