This paper presents a flexible and portable digital framework for Built-in Self-Test (BIST) and calibration of RF/analog circuitry. Novel to the proposed testing framework, is a reusable, flexible, drop-in IP core, composed of a centralized custom processing engine with data path, memory architecture and instruction set optimized for efficient execution of compute intensive test and calibration algorithms. The innovative BIST engine is complemented with a calibration and test sequencing methodology exploiting the embedded test hardware, to dynamically correct for transceiver imbalances and non-idealities, as well as to estimate performance parameters such as Error Vector Magnitude (EVM). The engine has been integrated with a WiFi transceiver in a 32 nm SoC test chip to demonstrate the functionality of this framework. This implementation covers an area of 0.63 mm2 and provides similar performance (e.g., improvements up to 10 dB in EVM for Rx IQ imbalance compensation) to off-chip testing without relying on expensive equipment.