If a credit card company offers you $500 for making $1500 in purchases within the first 3 months, is that taxable income?
No. If the reward is contingent on spending, then it is not considered taxable income. This is true of cash-back, points, and sign-up bonuses that are based on spending (Spend $x in first x months).
Edit: Seeking a better IRS source, the below has to do with personal use of rewards from business spending, but a more specific source may not exist, there are indeed unwritten tax rules that have been formed based on vaguely related written rules.
IRS Bulletin No. 2002–10 is referenced as the basis for this rule, but it is specifically regarding personal use of frequent flier miles earned through business travel.