I was in the Army and got arrested for shop lifting. I went through processing at the MP station, wasn't convicted or anything. Only some military discipline with a field grade article 15 and ended up getting discharged under honorable conditions. Now I am going through the police academy and the applications ask for any arrest information. I would prefer to avoid bringing that up... Is there anyway the arrest wouldn't be on my record being that I didn't get convicted?

If you got a Article 15, then there is a record, you may not call it convicted, but the Army will since there was punishment

So is that something that would prevent me from becoming a Law Enforcement Officer in the future? If it's not a conviction and I wasn't have to go to court or do any jail time I should be good right?

As Fr Chuck put it, "... you may not call it convicted, but the Army will ...". Police agencies will also consider it as such when you apply.