This goes back to the mid-ninteenth century. The letter R was used by morse operators to signify "message received". During WW2, the US phonetic alphabet word for the letter R was ROGER (prior to 1941, it had been ROBERT). This coincided with the widespread use of two-way voice communications, whereas previous radios were generally morse. So, ROGER was cemented as "message received" even after ROMEO became the word for the letter R in the 1950s.

ROGER is a procedural word, or proword. Prowords have very specific meanings in radio communication to both keep transmissions short and simple, and to reduce confusion. Other common prowords are WILCO ("message received, will comply"), OVER ("I am done transmitting, awaiting reply"), OUT ("I am done transmitting"), and BREAK ("short pause between message portions").