A cop made me hang up my phone to search and arrest me

Yes,they can do pretty much anything they want during an arrest.If you don't comply then they will add resisting arrest to your charges.

Isn't it against my civil rights?

We would need to know the circumstances. But if there was probable cause to make a search and arrest, then yes he can order you to terminate the call.

Isn't it against my civil rights?

You are allowed a phone call after your arrest and your booking but not while you are being arrested.That is not a civil right.

Even if it were,you would be hard pressed to do anything about it.

Isn't it against my civil rights?
No. When you came under suspicion and were arrested, your civil rights changed. Here are the rights you have when arrested:

Getting Arrested Checklist: Have My Rights Been Violated? - Learn About the Law (http://public.findlaw.com/civil-rights/more-civil-rights-topics/institutionalized-persons-discrimination-more/le5_e.html)

Ok, if they are going to arrest you and you refuse to obey the lawful orders of the officer, he will throw your phone to the ground, and then you after it, and handcuff you.

If fact if you are stopped for traffic stop and continue to talk on the phone when the officer is trying to talk to you, expect him to take your phone and hang it up, and find several more tickets to write you