For achieving that data structure, first, you have to perform the splitting and then use the cbind():
do.call(cbind, split(df, df$`R/C`))
# RR1.R/C RR1.DD RR1.CC1 RR1.CC2 RR2.R/C RR2.DD RR2.CC1 RR2.CC2 RR3.R/C RR3.DD RR3.CC1 RR3.CC2
#1 RR1 a 36 37 RR2 e 37 38 RR3 i 89 90
#2 RR1 b 21 22 RR2 f 17 17 RR3 j 79 80
#3 RR1 c 24 25 RR2 g 16 16 RR3 k 26 26
#4 RR1 d 196 198 RR2 h 48 51 RR3 h 48 51
df <- structure(list(`R/C` = c("RR1", "RR1", "RR1", "RR1", "RR2", "RR2",
"RR2", "RR2", "RR3", "RR3", "RR3", "RR3"), DD = c("a", "b", "c",
"d", "e", "f", "g", "h", "i", "j", "k", "h"), CC1 = c(36L, 21L,
24L, 196L, 37L, 17L, 16L, 48L, 89L, 79L, 26L, 48L), CC2 = c(37L,
22L, 25L, 198L, 38L, 17L, 16L, 51L, 90L, 80L, 26L, 51L)),
class = "data.frame", row.names = c(NA, -12L))