In this paper, the issue of self-compacting concrete (SCC) with the addition of polyethylene terephthalate (PET) recycled aggregate is addressed. The PET utilized was a waste fraction in the PET-bottle-recycling process. The implementation of waste in concrete mixes has a positive impact on their environmental and social profile; however, technical requirements are not necessarily met. In this investigation, PET was used as a substitute for fine aggregate in quantities ranging from 0 to 20% in increments of 5%. Both the flow properties of SCC mixes and the hardened SCC properties (compressive strength, splitting tensile strength, modulus of elasticity, and Poisson ratio) were investigated. Additionally, non-destructive tests (ultrasound and sclerometric) were performed to determine the correlation curves. The research revealed that both the flow properties and the parameters of the hardened concrete deteriorated with the PET content. Concrete with 20% PET replacement did not meet the self-compacting requirements and its compressive strength decreased by almost 50%. However, it was noted that replacing fine aggregate with PET aggregate in the amount of 5% did not significantly alter the concrete parameters and could be an attractive alternative to traditional concretes. Based on non-destructive testing, correlation curves were constructed that could be applicable to the future quality assessment of self-compacting concretes with recycled PET aggregate.