Most likely, you will not. If the case was dismissed, then you will have no problem, if you were convicted (or even given a withhold of adjudication, which for Immigration purposes is the same as a conviction) then it will depend on the amount of the theft, and if it was charged as a misdemeanor or a felony. The guidelines for DACA state that the person cannot be convicted of "a felony, significant misdemeanor, three or more other misdemeanors, and do not otherwise pose a threat to national security or public safety". If the shoplifting was charged as a misdemeanor, it will likely not be considered a significant misdemeanor.
I'd recommend taking your criminal paperwork to an immigration attorney. To start with, you're not even sure if the case was dismissed or not. There are many ways a criminal court can resolve a charge that might "feel" like a dismissal, but for immigration purposes, are not a dismissal.
For example, the judge might accept your guilty plea, and then sentence you to time in jail, but then immediately suspend all of the sentence. So, you walk out of court and never have to go to jail--but you still have a conviction and sentence to jail for immigration purposes.
Or perhaps the judge accepts your guilty plea, but doesn't pronounce you guilty, and instead puts you on a period of probation, and at the end of that probationary period, assuming you complied with all the terms, she allows you to take back your guilty plea. For most purposes, you were never convicted--because the judge never formally pronounced your guilt. But for immigration purposes, you do have a conviction--because you admitted your guilt to the judge, and she placed some limitations on your liberty.
If you truly don't have a conviction, then you're probably fine with DACA. If you do have a conviction, however, then a more careful analysis will need to be made to assess eligibilty.
I suggest a meeting with an attorney. Take all of your paperwork to the meeting.
Samuel Ouya Maina, Esq. 415.391.6612 email@example.com Law Offices of S. Ouya Maina, PC 332 Pine Street, Suite 707 San Francisco, CA 94104