"Rotating" normally implies more than two; rotate (applied to an office, as here) means "pass to each member of a group in a regularly recurring order" (Oxford). In this case there are just two countries involved, so I think the word is "alternating" rather than "rotating".

The rest of it says "dos turnos de un año cada uno", which clearly means "two terms of a year each". I would translate it like that, though "two one-year terms" would be fine.

The point of this is that normally the Secretary General of Unasur serves for two years, renewable once.
http://en.wikipedia.org/wiki/Secretary_General_of_UNASUR
In Quito they decided to divide the two years between the two countries, serving one year each. The background to this was the dispute between Colombia and Venezuela over accusations that Venezuela had been harbouring Colombian terrorists.