I think you could say income has an indirect bearing on your FICO score when you are first starting your credit history (no previous credit history).
When you apply for a credit card for the very first time, you have no credit history so they need something else to determine your initial line of credit: your annual income. It's the debt to credit ratio that has an impact on your FICO score. So logically if you have a higher income, it won't impact your FICO score directly but it may impact your initial credit line and therefore your debt to credit ratio which does directly impact your FICO score.
i.e. If there are two fresh credit applicants with no previous credit history whatsoever. (this is just an example; this is not to say a person with such income will necessarily have these exact figures.)
Person A
$50,000/year
Bank gives Initial credit line of: $5,000
Person B
$25,000/year
Bank gives Initial credit line of: $2,500
Let's say person A & B both spend $1000.
Person A's debt to credit ratio = 1/5 = 20%
Person B's debt to credit ratio = 2/5 = 40%
That means person B has double the debt to credit ratio that person A does... and person B's debt is nearly half of his alotted credit! That does affect FICO score.
Of course, this can all change depending on how well person A & B pay back their debt. If person B has a higher debt ratio but pays back diligently while person A has a lower debt ratio but misses payments and is inconsistent, person B will get a credit line increase quickly so beyond that it's anyone's game so I think arguably your income indirectly impacts your FICO score initially but has less and less impact on your credit score as it builds since how much you make really has no bearing on willingness and diligence in repayment.