There were quite a few, especially during the Crisis of the Third Century. For a few decades the most common path to becoming emperor was service in the military, followed by a revolt against the sitting emperor(s). This opened the office up to people of more diverse backgrounds than just members of the Julio-Claudian, Flavian, Antonine or Severn Dynasties. Officers in the legions who went on to become emperor such as Maximinius Thrax, Licinius, Galerius or Aurelian all likely came from peasant or similarly lower class backgrounds. Even Diocletian was considered very low born, although its unclear what his family did for a living.

In the Byzantine period, Justinian's uncle Justin I was born a peasant in the Balkans. Similarly to the Crisis of the Third Century, during periods where the throne was contested by rebelling generals (such as during the end of the Heraclian dynasty), men of peasant backgrounds were more likely to make it to the top. While the sources aren't clear enough to say for certain, emperors like Leontios or Tiberius III may have been peasants before the joined the army.

Sources: "The Complete Roman Army" by Adrian Goldsworthy (I know some historians have issues with him, but I don't the peasant origins of many of the so-called "barracks emperors" is much in dispute)

"The Cambridge History of the Byzantine Empire" by Johnathan Shepard