Can TSA have me arrested simply because they found a large amount of cash in my carry-on bag?

While it is legal to travel with any amount of cash, TSA could hold you for investigation by federal or local law enforcement authorities if you are asked to account for the cash and they are dissatisfied with your explanation.  TSA screening officers could consider the large amount of money as possible evidence of illegal activity – e.g., a violation of customs reporting, drug trafficking or money laundering).  You should expect your security processing to be delayed by a private TSA screening; there must be a witness present. 

If possible, be prepared to explain (and perhaps provide documentation of) the source of the cash and the purpose(s) for which you are carrying it.  The TSA officer who conducts the screening has been trained to assess passenger reactions to such questions; if your responses or behavior cast doubt upon your credibility, or if you fail to be forthcoming, the TSA officer has the authority to detain you for a referral to law enforcement authorities.

If you believe that TSA personnel behaved illegally or inappropriately in detaining you and/or transferring you to the custody of law enforcement, you can file a complaint with the Department of Homeland Security Traveler Redress Inquiry Program.  If you believe their conduct was particularly outrageous, you may want to consult with an experienced civil litigation attorney before you make any further statements to any government representatives or entities.