You could use a diode bridge. A silicon bridge would lose you nominally 1.4v, a schottky bridge 0.7v.
A better solution would be to use a MOSFET bridge, which being resistive when on would result in near zero drop.
For a range of input voltages > Vgs(th) but < Vgs(max), the following should work ...
simulate this circuit – Schematic created using CircuitLab
Four complementary FETs are shown, with their intrinsic body diodes. Neglecting any FET operation, the body diodes form a normal bridge rectifier.
Now consider Va high, Vb low. Va high turns on M1. Vb low turns on M4. M1 shorts D1, which is conducting anyway to connect Vb to the output. M4 shorts D4, which is conducting anyway to connect Va to the output. Result, happiness, as long as Vin exceeds Vgs(th) for both types. Obviously the complementary thing happens for Vb high.
Another way to look at it is to notice we have two complementary FET inverters.