The past has involved many myths about the existence of giants. Various colonizers and travelers, for example, reported giants among the indigenous peoples of the Americas (eg "Giant Amerindians: Fact or Fantasy?", 1997). And while a lot of travelers and storytellers have believed in various giant myths in the past, how common was it for archaeologists themselves to believe in giants in the 17th, 18th, 19th, and early 20th centuries? Are there any archaeologists who believed this? And if so, in what context did they believe it? Did they claim to have discovered giant fossils; did they claim various indigenous peoples had giants among them; how did their contemporaries react?
If we look through some of the accounts of giants, such as the Patagon we find that the 13 to 15 foot giants were mostly the belief of some sea explorers that claimed to have seen them.
The Book of Giants was an apocryphal book which was mostly believed by religious adherents.
If we take the claims of Siah Khan being 11ft10, we find that once investigated, doctors believed him to only be 8ft6.
The Giant of Castelnau was first reported by an anthropologist as being 11ft6. Later reports that they represented a very tall race came from a zoologist. To date I am not sure if the claims have ever been debunked by modern science.
There is also the case of Orestes from Greek mythology. However excavations of caves where Orestes remains were reported to be found, found only bones of mammoths, elephants, deers, bovids and cataceans.
Other reports, such as that of Emperor Keiko being 10ft2, or Goliath being 9ft9, fall into the exact same categories as those mentioned above, and no archaeologists were ever mentioned, and apart from the case of the Giant of Castelnau which would require further investigation to find out what modern science has to say about it, the belief in giants do not appear to have ever been a very common archaeological or scientific belief.