Can a Senior NCO order a lower enlisted (Private) to hand over their personal cell phone?

Confiscate legal personal property? NO.
But absolutely order the SM to not use it, have in their hand in any way shape or form during duty hours unless on a prescribed and authorized break.
And if the SM is so inclined, Id be happy to take it off your hands and store it for you so do not run afoul of that requirement...... Your choice Soldier,,,, but you have been given a lawful order.. If you so much as fall down and have the phone fall out of your pocket and into your hand.. you are going to have problems.
So what is your preference? Maintain it and not touch it? or lock it and drop it in this box here till lunch time?

That said you did not provide much in way of context.
Is the SM and NCO standing near a restricted area that phones are not allowed?
Has the phone been used in a manner that violates policy, regulations, a lawful order?
Is the NCO providing what may technically be not allowed, but it is a leadership decision in effort of dealing with an issue short of UCMJ?

I did that a fair amount for minor infractions of the bone head nature..... "You can deal with me and no complaints or you can deal with the commander and UCMJ..which is it and you can not change your mind after"

I only offered that on things that no one got hurt, no crime committed and no malice intended.
Drunk SM peed on the company "rock" last night
Pissed off SM through a wrench in the MP, broke a window
SM backed up a vehicle without a ground guide in an empty parking lot at night and hit a pole.

I can see a number of situations where this might occur.
Most of them involve being told to put the damned thing away and concentrate on the task at hand... and SPC Tentpeg not getting the message.
As a rule, I don't lightly take things away from people. It breeds resentment. And it makes the subordinate feel like a child.
But I do hand out opportunities for quality time with some Sr NCOs if Joe can't figure it out the easy way.

Really need more information before giving a ye or nay on this one. As far as the word order is concerned, under the correct circumstances this is entirely warranted. Many people have already posted that an order cannot be given by an NCO, they are mistaken. There are two kinds of orders, direct and lawful. Direct orders can only be given by officers, however, lawful orders can be given by NCOs. Under certain circumstances, it could be a lawful order to surrender a personal cellular device.

Ya know, that's a really interesting question...not a clue as to the answer, obv, though, as I'd said, an interesting question nonetheless, certainly....

Didn't have none of those fancy cell phones in my day. I would tell the troops that the cell phones were a distraction and were not to be in the training area. Then I would drop hints as to why no one can have a phone.

The noncom can direct, but not order anything except burgers and fries. Orders are relegated to commissioned and warrant officers of all grades.

Remember this opening sentence? "You are hereby directed to report to your Selective Service representative . . ."

Must've been a noncom writing that letter.

It's Article 134. I know I'm late to the party, but damn! If you have a phone and you can't have a phone and do your duty like you're supposed to you're gonna have to put the phone somewhere you can't get to it. Why is this even a question? What is happening in the military? The military has rules, and order, and discipline! If you don't like that crap don't enlist! Go find a job in the real world that'll let you play with your phone half the damn day!

He can order him to turn it off and go back to the barracks and put under lock and key

Was troop issued that phone? Answer yes. Did troop buy the phone on his own? Answer non-military issue, not approved. Yes.

Yes, depending on the situation.