The fortification of staple foods and the exploitation of agri-food by-products are the goals of modern food technologies. In this study, we prepared fortified pasta by replacing semolina flour with 5%, 10%, and 15% dried red chicory by-product powder (RCP), rich in fiber (27%) and healthy bioactive compounds (4.3%). The UHPLC-DAD-HRMS indicated hydroxycinnamic acids (HA), flavonoids (F), anthocyanins (A), and sesquiterpene lactones (SL) as the main bioactive compounds of RCP. The extraction recoveries of phenolic-fortified pasta (ranging from 0.2 to 13% for HAs to 5–28% for Fs and < 0.2% for As) suggest a high affinity with the semolina components, likely gluten or starch. The addition of RCP influenced (p < 0.05) the pasta's technological properties by inducing an increase in cooking loss, fully cooked time, and a decrease in the swelling index. The texture analysis showed that firmness and adhesiveness increased in the fortified sample. The sensory characterization showed a greater perception of vegetable and bitter flavor with increasing fortification levels. The RC15 sample had optimal technological, nutritional, and sensory characteristics. In conclusion, RCP could be an ingredient used to produce pasta with high fiber and bioactive compounds.