The Census of 1850 and 1880 have full counts (100% sample) available, but 1860 and 1870 only have 1.2% samples available. Are they being digitized currently or are they available somewhere else or only by request? Thanks.
This site is invaluable for historic census data:
It combines many Census papers on the foreign-born population and, in the process of doing so, lists total population (native and foreign-born) by state and census region for each decade from 1850 to 1990. One of several tables cited in the report, “Table 13 - Nativity of the population, for regions, divisions and states, 1850 to 1990” may be overkill but it certainly should answer your question.