I remember when I first came across this word, I thought it was pronounced /'sɜr-dʒint/ (SER-jeent). Now I am curious as to why the first syllable is pronounced /sar/ rather than /sɜr/. I looked at the etymology, and found that the word has always had either sir or ser at the beginning, never sar. To top that off, sergeant comes from the Old French sergent, from Latin servientem meaning serving, the same root word that we get the word servant from. To my knowledge, servant has never been pronounced /'sar-vənt/. Why and since when has sergeant been pronounced sargent?
Per the Naval Historical Center: