The TI-89 is a CAS graphing calculator in a TI-89 model family that College Board identifies as prohibited for SAT use.
The current SAT calculator policy is not a simple approval list for every graphing calculator. College Board allows graphing, scientific, and four-function calculators only if they satisfy the restrictions, and the central restriction here is CAS. The TI-89 is recorded in this guide as a CAS graphing calculator with symbolic algebra capability. College Board's prohibited calculator examples include Texas Instruments model numbers beginning with TI-89, so this verdict treats the TI-89 as banned for SAT Math. The conclusion is intentionally practical: it does not matter that the device is familiar, old, powerful, useful for calculus, or capable of ordinary numeric calculations. It also does not matter whether a student plans to avoid symbolic features. The model family itself falls into the prohibited CAS category, so the safer test-day answer is to use Bluebook Desmos or a non-CAS handheld calculator.