Iron is not floating free in the blood, it is part of a larger molecule known as Hemoglobin. These molecules are what fills red blood cells, and eat one contains 'heme' groups with Iron. The propensity of Iron to interact with oxygen (by rusting or 'oxidizing' to become Iron Oxide) is what allows the mostly organic 'heme' group to hold tightly onto oxygen, and deliver it throughout your body.
This is also why the blood in your iron is not disturbed by the powerful magnets in an MRI.