If the background screening tool that is used pulls information from the arresting police department's public records reports, it is possible that your arrest could show up. However, this would most likely occur if you were arrested by a large metropolitan police department or state highway patrol officer.
If you were arrested in a smaller city/town or rural area by a smaller PD, it would likely not be an issue for you.
Most background checks, especially for lower level jobs, probably would not go into that level of detail.