Are there any birds that could theoretically carry a human on top of them?

 

A picture of men racing on ostriches in okhlahoma. 

Largest known flying bird ever: Argentavis - Wikipedia had a wingspread estimated at 6 to 7+ meters (19 to 20+ feet); with some estimates closer to 24 feet.

They lived in and around the southern Andes during the late Miocene to early Pliocene and weighed approximately 70 to 72 kg (154 to 159 lb).

Although this bird had a larger wingspan its wings had a higher aspect ratio (they were narrower for their length) and was only half the overall body mass:
Pelagornis sandersi - Wikipedia
http://www.sci-news.com/paleontology/science-pelagornis-sandersi-largest-ever-flying-bird-02046.html

For comparison here is a close relative along with some other contenders including the Ailornis of N. America a likely match for the legendary Thunderbird:

Pterosaurs got considerably larger but they weren’t birds. Argentavis had a wing loading of 1.77 lbs./ sq. ft. (c. 11.5 kg/m²) and lifting a 170 lb. human male would more than double that. Additionally it has been speculated that they were slope soarers who could only get airborne by jumping from a high mountain and gliding to the nearest thermal which they depended on for lift.

 There are no living flying birds in existence that are capable of carrying a grown man. The largest living flying bird today is the Andean Condor, weighing 26 pounds and having an 11 foot wingspan. It is not the heaviest though.

Andean condor

Andean condor being released

A close contender is the Kori Bustard, which weighs in at about 46.3 pounds and a wingspan of nine feet. The Kori Bustard is the heaviest flying bird but the Andean Condor has the greater wingspan.

Kori bustard in flight

Kori Bustard

Even with such a wingspan these large birds are not able to do much more than soar much less carry the additional weight of a man. Their metabolism is not capable of providing enough energy for it. The most observed weight a bird was observed carrying was a bald eagle lifting 16 pounds of mule deer. A mule deer’s average weight is between 100 and 300 pounds so the above record was not the entire animal. Eagles have also been observed carrying goats or lambs off cliffs, but that is a downward soar before landing to eat the prey. Lambs and goats depending upon their age can weigh 6 pounds to 30 pounds or so. A heavier larger animal will require a different hunting strategy rather than simply plucking one off the ground.

Large flying birds are not capable of carrying a grown man in flight.

Read more at Quora