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.
The complete count samples for 1860 and 1870 are still under construction by the IPUMS USA Team. As noted here, there is a goal to have these samples released by 2020. Beyond this broad goal, I can’t be more specific about when these data will be available.