The Bureau of Labor Statistics publishes the CPI once a month at 8:30 am New York time. Each item in the basket counts according to how much households spend on it, and housing is by far the largest part.
Markets react to the surprise, not the number itself: what counts is the gap between the figure and the forecast. A higher reading than expected can move stocks, bonds and Bitcoin within seconds, because it changes what traders expect from the Federal Reserve.
Example
On September 13, 2022, August CPI came in at 8.3% against 8.1% expected, and the S&P 500 fell 4.3% that day.