Beth, I did not find any Rozetta/Rosetta etc. in the 1870 Census of Fulton County. I only found three Spencer families so I am listing them.
1870 Census, Fulton County, Rochester Twp., IN D215 F215 Spencer, Elizabeth 59 ME Spencer, Augustus 19 IN
1870 Census, Fulton County, Rochester Twp., IN D144 F144 Spencer, John M. 45 OH Farmer Spencer, Louis R. 42 NY Spencer, Austin J. 19 IN Farm Laborer Spencer, John W. 17 IN Farm Laborer
1870 Census, Fulton County, Wayne Twp., IN D127 F127 Spencer, John B. 31 NY Farm Laborer Spencer, Hariett 22 IN Spencer, Edward 2 IN Spencer, Charles 8/12 Oct. IN
I also did a look in the 1860 Census of Indiana and found two Rosetta/Rozilla Spencers.
1860 Census, Allen County, Perry Twp., Leo, IN D767 F747 Spencer, Rosetta 6mths IN>in home of Spencer, Elijah 24 NY Farmer R-600 P-75 Spencer, Myra 15 IN Spencer, Marietta 5 IN Spencer, Leavit 3 IN
1860 Census, Steuben County, Steuben Twp., Pleasant Lake, IN D531 F545 Spencer, Rozilla 12 IN School>in home of Spencer, J.H. 51 Conn Farmer R-3000 P-300 Spencer, Lucinda M. 24 MI Housekeeper Spencer, Mary 19 IN Housekeeper Spencer, Matilda 17 IN Housekeeper Spencer, Norman 14 IN School Spencer, Ellen 10 IN School Spencer, Roswell 1 IN