I have seen rental phones advertised at some of the airports. Not sure of the cost, though.
If you have a GSM quad band phone with SIM, you can get a pre-paid sim card. I would check with your US provider and ask if they can forward your US calls to the international number if you provide it to them. (Likely a cost for this, too. Talk isn't cheap!
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Depending on how long you will be in Brazil, how many folks will be calling you from the US? If only a few, give them the number of your Brazil SIM if you get one. (Call one person in the US and ask them to let others know) Even getting a call on your US based phone will cost you more, as will making them. I have international calling and roaming on my US plan, but getting the local SIM is cheaper.
Depending on your US provider, your US SIM may automatically pick up a local carrier, but dialing can be complicated. For instance, you would not be able to automatically call your voicemail. At least that was my experience with AT&T.
If you use up the time on the prepaid Brazil SIM card, you can go to numerous places in Brazil to replenish it.
And with the Brazil SIM, you are only charged for outgoing calls, not incoming calls!!! Another thing to consider is if this is a one time trip or will you be making more?
Additionally, will you be making calls in Brazil? A local isn't going to want to call you using your US phone number.
There are several providers in Brazil, TIM, Oi, VIVO to name a few of the major ones.
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