There are two theories. One is outlined by @Critter-3 that you can only deduct the extra cost associated with the business.
The other argument is that you can deduct a percentage of the cost, even if there is no extra cost, but you must have some kind of reliable written record to support your business use percentage. Interestingly, I followed the first recommendation until I read a tax court case about two university professors who tried to deduct a percentage of their flat rate home internet as a work expense. The tax court noted that the deduction would have been allowed except the professors had no written or other reliable documentation to determine the work-related percentage. So it seems that at least some tax court officers would allow the deduction even on a flat rate plan, as long as you had proof.
You can also list your phone as a business asset for depreciation, using the same percentage and assuming you have the same reliable records. If you sell the used phone later, you may have to deal with depreciation recapture. When you place the phone "in service" for the business and list it on your tax return, the cost basis is the actual cost of the phone, or the present fair market value at the time it is placed in service, whichever is lower.
(This also raises a side point. If you are paying for your phone on installments as part of your bill, you can't deduct the cost of the phone as a monthly business expense, you can only recover the cost of the phone via depreciation. So if your bill is $100 per month and you use the phone 50% for business, but $30 per month is the installment plan to buy the phone, your expense deduction would be $35, not $50 per month. You recover the cost of the phone by listing it as an asset and claiming depreciation.)
