We introduce the RadixStringSpline (RSS) learned index structure for efficiently indexing strings. RSS is a tree of radix splines each indexing a fixed number of bytes. RSS approaches or exceeds the performance of traditional string indexes while using 7-70$\times$ less memory. RSS achieves this by using the minimal string prefix to sufficiently distinguish the data unlike most learned approaches which index the entire string. Additionally, the bounded-error nature of RSS accelerates the last mile search and also enables a memory-efficient hash-table lookup accelerator. We benchmark RSS on several real-world string datasets against ART and HOT. Our experiments suggest this line of research may be promising for future memory-intensive database applications.