User dawnhunter of Reddit writes in the /r/Showerthoughts/ thread called In the word "scent", is it the S or the C that is silent?:
Here's what a google search brings up:
late Middle English (denoting the sense of smell): from Old French sentir ‘perceive, smell,’ from Latin sentire . The addition of -c- (in the 17th century) is unexplained.
So the c is silent and also shouldn't really be there.
Also, further down the thread, another comment says:
The 'c' was probably added because that was the style at the time.
Originally a hunting term. The -c- appeared 17c., perhaps by influence of ascent, descent, etc., or by influence of science. This was a tendency in early Modern English, also in scythe and for a time threatening to make scite and scituate.