Hi Samara -
I would take one of two approaches depending on what you mean by the urban/rural character. The USDA classifications are based on commuting patterns are reflect the proximity to large urban areas. The Census Bureau's urban/rural area are based on the rural nature of the immediate environment. A rural area near a large city could be classified as rural using the Census measure and urban using the USDA measure.
1) Proximity to urban areas: take the USDA's rural-urban commuting area (RUCA) tract-level codes, link them with the 2010 Census tract to 2010 PUMA relationship file and a census tract population file, and calculate a population-weighed RUCA value for the PUMAs. To reduce the 33 RUCA codes to a smaller set of categories, see
depts.washington.edu/.../ruca-uses.php 2) Rural nature of the immediate environment: take the Census 2010 P2 table, link it with the 2010 Census tract to 2010 PUMA relationship file, and calculate the percent of the population living in rural and urban areas in the PUMA.
The 2010 Census tract to 2010 PUMA relationship file can be found at
www.census.gov/.../centract_rel.html -- Dave Stinchcomb