The composition of self-compacting concrete (SCC) contains 60–70% coarse and fine aggregates, which are replaced by construction waste, such as recycled aggregates (RA). However, the complexity of its structure requires a time-consuming mixed design. Currently, many researchers are studying the prediction of concrete properties using soft computing techniques, which will eventually reduce environmental degradation and other material waste. There have been very limited and contradicting studies regarding prediction using different ANN algorithms. This paper aimed to predict the 28-day splitting tensile strength of SCC with RA using the artificial neural network technique by comparing the following algorithms: Levenberg–Marquardt (LM), Bayesian regularization (BR), and Scaled Conjugate Gradient Backpropagation (SCGB). There have been very limited and contradicting studies regarding prediction by using and comparing different ANN algorithms, so a total of 381 samples were collected from various published journals. The input variables were cement, admixture, water, fine and coarse aggregates, and superplasticizer; the data were randomly divided into three sets—training (60%), validation (10%), and testing (30%)—with 10 neurons in the hidden layer. The models were evaluated by the mean squared error (MSE) and correlation coefficient (R). The results indicated that all three models have optimal accuracy; still, BR gave the best performance (R = 0.91 and MSE = 0.2087) compared with LM and SCG. BR was the best model for predicting TS at 28 days for SCC with RA. The sensitivity analysis indicated that cement (30.07%) was the variable that contributed the most to the prediction of TS at 28 days for SCC with RA, and water (2.39%) contributed the least.