Steel structure designers frequently encounter the need to reinforce hot-rolled compressed steel elements. This is particularly common in the case of compressed truss bars in steel truss girders. Typically, reinforcement is designed using bars or flat bars welded to the compressed element. However, welding technology is not always feasible in existing and operational steel halls due to fire safety concerns. To address this challenge, researchers investigated alternative reinforcement methods using bonded steel and CFRPs (carbon fiber-reinforced polymers/plastics) tapes. Laboratory tests and numerical analyses were conducted. Eleven 1.5 m long specimens made of 50 × 50 × 4 angle iron from S235 steel were subjected to axial compression testing. The test samples included three unreinforced samples, three samples reinforced with steel tape bonded using SikaDur-30 adhesive, and five samples reinforced with CFRP tape (SikaDur-30 adhesive was used for bonding in three cases, and 3M VHB GPH-160GF tape in two cases). The research conducted indicates that reinforcement using bonded steel tapes is the most effective method for limiting vertical displacements and deformations, as well as increasing the load-bearing capacity of the tested angles by 28.6% compared to the reference elements. Considering the high cost of composite tapes, this is valuable information from an economic analysis perspective. The absence of steel tape delamination suggests that the bonding technique can be successfully employed in this reinforcement method and can replace welding, for example in facilities where there is a high fire hazard.