DHS Cybersecurity On-the-Job Training and Employment Apprentice Program Act This bill requires the Department of Homeland Security (DHS) to establish a DHS Cybersecurity On-the-Job Training and Employment Apprentice Program to identify and train DHS employees for cybersecurity work. The Cybersecurity and Infrastructure Security Agency within DHS must lead the program. Among other things, the agency must (1) track the status of cybersecurity positions at DHS, (2) develop a program curriculum, and (3) recruit DHS employees for the program.