At 0607 GMT, the rand traded at 19.3300 against the dollar, the same level as its previous close.
The census is the fourth in post-apartheid South Africa and the first in over a decade.
On Monday the rand tumbled as violence in the Middle East stoked risk aversion on global markets.
"In a world of so much uncertainty, it is not surprising to see the (dollar-rand pair) unable to adopt any clear-cut directional momentum. It is trading in a tight range, and investors are waiting for the dust to settle," ETM Analytics said in a research note.
(Reporting by Alexander Winning; Editing by Andrew Heavens)
