By all accounts the Angels farm system is thin and, well, it really is. I've got 36 names here and some of them are pushing it.

Los Angeles Angels 36 players

Yency Almonte RHP
R.J. Alvarez RHP
Cam Bedrosian RHP
Kole Calhoun OF
Ryan Chaffee RHP
Chevez Clarke OF
Mike Clevinger RHP
Kaleb Cowart 3B
C.J. Cron 1B
Steve Geltz RHP
Randal Grichuk OF
Wade Hinkle 1B
Eswarlin Jimenez LHP
Luis Jimenez 3B
Sherman Johnson 2B
Taylor Lindsey 2B
Matt Long 2B-OF
Nick Maronde LHP
Carlos Ramirez C
Andrew Romine SS
Jose Rondon SS
Michael Roth LHP
Mark Sappington RHP
A.J. Schugel RHP
Reid Scoggins RHP
Brandon Sisk LHP
Michael Snyder 1B
Wendell Soto SS
Dave Spiwack LHP
Eric Stamets SS
Andrew Taylor LHP
Dan Tillman RHP
Jonathan Walsh OF
Travis Witherspoon OF
Austin Wood RHP
Zach Wright C
Alex Yarbrough 2B