Researchers observed adult male botos carrying these objects while surrounded by females, and thrashing them on the water surface aggressively.
Writing in the journal Biology Letters, they say such behaviour has never before been seen in any marine mammal.
The boto lives in only two rivers, and numbers are thought to be declining.
A group of British and Brazilian researchers studied the dolphin's unique courtship behaviour over three years in the Mamiraua Reserve, a flooded rainforest area on the Amazon.
"You see them coming up with bits of wood or lumps of rock in a very ritualised manner," recalled Tony Martin from the Sea Mammal Research Unit at St Andrews University.
They may be fairly numerous now, but they're going downhill fast and we can't see any end to it
"They would also throw it or smash it against the surface, and it does appear that the waving around and bashing is to impress the ladies; but at the same time there's a lot of aggression between adult males, and we have to infer that's part of it."
Professor Martin's group established that rock carrying and branch thrashing were almost exclusively the preserve of adult males, and that they did it more when lots of adult females were present.
Although the males were more aggressive towards each other at these times, they were never seen to hit each other with the rocks or plants.
Three years ago, scientists found bottlenose dolphins in Australian waters carrying pieces of sponge, either to help with foraging or to defend against predators.
But using objects for socio-sexual display is a novel finding.
"I naively imagined this kind of thing was seen in other mammal species," said Professor Martin.
"But I was quite surprised when I consulted friends and colleagues, and it turns out that only chimps do anything similar - and that's much less sophisticated."
How and why the boto evolved the behaviour is unclear; although as cetaceans communicate largely with sound, it appears likely that the displays also create an impressive auditory impact on females, rival males, or both.
Hooked on boto
This research stemmed from a larger project, Projeto Boto, aimed at conserving the Amazon dolphin and its habitat.
River dolphins are among the most threatened of all cetaceans; the baiji, a native of the Yangtze in China, may already have gone extinct in the last two years, while numbers of the Indus or blind river dolphin of South Asia are believed to be down to around the 3,000 mark.
Botos are increasingly turning up harpooned, their flesh used for bait
But the future does not appear secure. The Red List concludes that the boto is threatened by dams (causing fragmentation of their habitat) and pollution, such as from mercury used in gold mining.
"With growing human populations in Amazonia and Orinoquia, the conflicts between fisheries and dolphins are certain to intensify", it notes.
Projeto Boto has found that fishermen are increasingly catching the dolphins for use as bait to catch a fish, the piracatinga, which usually feeds on dead flesh.
Meat from the caiman, a close relative of the alligator, is also used for this purpose.
Projeto Boto scientists are regularly finding dead dolphins, either harpooned or entangled in ropes.
"We lost half of the animals from our study area in just five years," said Tony Martin.
"They may be fairly numerous now, but they're going downhill fast and we can't see any end to it."