Not true:
https://en.m.wikipedia.org/wiki/Census_of_Quirinius
Quote:Census of Quirinius
The Census of Quirinius was a census of Judaea taken by Publius Sulpicius Quirinius, Roman governor of Syria, upon the imposition of direct Roman rule in 6 CE.[1] The author of the Gospel of Luke uses it as the narrative means to establish the birth of Jesus (Luke 2:1-5),[2] but Luke places the census within the reign of Herod the Great, who died 10 years earlier in 4 BCE.[3] No satisfactory explanation of the contradiction seems possible on the basis of present knowledge,[4] and most scholars think that the author of the gospel made a mistake.[5]
https://en.m.wikipedia.org/wiki/Census_of_Quirinius