API to reverse geocode latitude, longitude to census tract?

You could do it locally instead of an online API. One solution with R: Census boundary data for the USA is available through TIGER at census.gov; if you're thinking about the US then you could download the US states and use a function to get the tracts. For example, using California and a random (or random-ish) point:

library(maps)
library(maptools)


tractLookup <- function(x, y, state) {
  pt <- SpatialPoints(data.frame(x = x, y = y))
  overlay.pt <- overlay(pt, state) # what index number does pt fall inside?
  return(census$TRACT[overlay.pt]) # give the Tract number from the census layer
}

Try it out:

california <- readShapePoly("~/Downloads/US_2000_Census_Tracts/tr06_d00_shp/tr06_d00.shp")
tractLookup(-123.123, 40.789, california)

Gives 0004, which is correct.

# Look at the map
plot(census)
map('state', c('California'), lwd = 2, col = 'green', add = F) # optional
points(-123.123, 40.789, col = 'red', lwd = 2)

This works, but takes 5 seconds on my Mac, which would probably be too much if you're going to do a lot of this; I suspect someone will weigh in shortly with a PostGIS solution that will be a million times quicker ...

In PostGIS, if you have a table of points, and the census boundary information that @Sminbamangu refers to you could calculate this using the following approach:

SELECT 
       c.census_tract, 
       p.point_id
FROM
       census_boundary as c,
       table_of_points as p
WHERE
       ST_Contains(c.geom, p.geom);

You can see the description ST_Contains here. This would return a table of the points, and the census tract where they are located.

As mentioned by @Simbamangu, this could easily done locally by just about any desktop GIS software on the market.

For free & open source, take a look at a "join attributes by location" in QGIS.

If you plan to need to do this repeatedly over time, you could consider putting the datasets into PostGIS and creating a spatial join (see this example in the online help). You can then visualize the results in QGIS.

You can use Geocodio to convert latitude/longitude coordinates to FIPS codes.

We don't have a reverse geocooding to FIPS example in our docs, but it works the same way as the forward endpoint. You can see an example here (note: this DEMO API key has a limit per day, so you may need to create a free API key to see this. The first 2,500 lookups per day are free, no credit card required.)

https://api.geocod.io/v1.6/reverse?q=38.9002898,-76.9990361&&fields=census&api_key=DEMO

You can also see all of the data returned here: https://www.geocod.io/docs/?python#census-block-tract-fips-codes-amp-msa-csa-codes

Disclosure: I am one of the founders of Geocodio.