Convert row names into first column

Or you can use tibble's rownames_to_column which does the same thing as David's answer:

library(tibble)
df <- tibble::rownames_to_column(df, "VALUE")

Note: The earlier function called add_rownames() has been deprecated and is being replaced by tibble::rownames_to_column()

A one line option is :

df$names <- rownames(df)

You can both remove row names and convert them to a column by reference (without reallocating memory using ->) using setDT and its keep.rownames = TRUE argument from the data.table package

library(data.table)
setDT(df, keep.rownames = TRUE)[]
#    rn     VALUE  ABS_CALL DETECTION     P.VALUE
# 1:  1 1007_s_at  957.7292         P 0.004862793
# 2:  2   1053_at  320.6327         P 0.031335632
# 3:  3    117_at  429.8423         P 0.017000453
# 4:  4    121_at 2395.7364         P 0.011447358
# 5:  5 1255_g_at  116.4936         A 0.397993682
# 6:  6   1294_at  739.9271         A 0.066864977

As mentioned by @snoram, you can give the new column any name you want, e.g. setDT(df, keep.rownames = "newname") would add "newname" as the rows column.