In addition the already mentioned GSL, there are two more I know of and which I have used for spline interpolation in C/C++: John Burkardt's spline library[1] and Netlib[2]. The pppack library from Netlib is Fortran code so you have to write a wrapper when using it from C++.
[1] https://people.sc.fsu.edu/~jburkardt/cpp_src/spline/spline.h...
[2] https://netlib.org/pppack/
EDIT: A quick internet search (in my case for cubic splines) gave more relevant results, so dependent on your needs, just look around: https://www.bing.com/search?q=cubic+spline+c%2B%2B