Does anyone know where I can find an algorithm, as well as an
R implementation of it, to carry out sparse principal component analysis (PCA)?
Another good package is the elasticnet package that Zou and Hastie put out. It has the function
Be careful to select a good value of $\lambda$, the sparsity parameter (or vector of them).
I would be curious to know which package ends up working better for you since the other package mentioned by @Stephan Kolassa is a year newer and is by Hastie's coauthor, Tibshirani.