I know defining a farm is tricky. I will, of course, take any definition available. If I could pick, I would say that if there is one person working full-time outside of a household, that household is not a farm, even if it grows food.
From the US Census, 1920 was the first census where more than half the population was considered Urban rather than Rural. This might be considered a rough answer to your question.
From IPUMS (click on "case count" here) we have the number of farm and nonfarm households in the United States from 1850 onwards (note comparability problems after 1950). In their 1% sample of the 1850 census, more than half of households are non-farm. However, the groups are close to equal size, so we can expect the equal split (in households) to have taken place sometime in the 1830s or 1840s. (However, we can expect farm households to be larger than nonfarm households on average, so that more than half of households lived on farms in 1850. If you are affiliated with an academic institution you can download the IPUMS data - samples of individual records going back to 1850 - and check this for yourself.)
As noted in the answer by Oldcat, it is easier to find statistics of rural and urban populations, but of course a large part of the rural population does not live on farms. More such historical statistics are here: https://www.census.gov/population/www/censusdata/hiscendata.html
You can research the question further by going through the individual census reports here to see if any report farm and nonfarm populations: https://www.census.gov/prod/www/decennial.html (rather large downloads).
To comply the comments I rewrote: While this is not a direct demographic data, GDP by industry can be a good indicator where the jobs are. Agriculture is primarily farms based, industry, service is primarily urban. It may not give an exact 50% point, but gives an idea. Also, the reason behind the demographic change is the shift of economy and majority of production (hence jobs) is now in service industry, some in makers.
Now one has to figure out what is the relative monetary value of the product of an industrial and agricultural worker. It is maybe slightly lower for agricultural workers, but especially if you go for historical data and big averages, on both side you find mainly people with minimal training at minimal wage. Let's see how the present situation, so it may help calibrate this estimation: http://data.worldbank.org/indicator/NV.AGR.TOTL.ZS It is clear that even in the poorest countries 40-50% coming from agriculture is extremely rare. You find many modestly developed country with large rural population at the 10-20 % segment.
I haven't found historical pre-ww2 GDP data, but even at 1947 the GDP coming from agriculture is still around 8% going down to 1% at a constant pace.
The two wars definitely gave huge boost to industrialization of the country, and also it triggered large demographic changes, so I would put the early 20th century and the two world wars as a major step toward urbanization.