You should probably detail your goals a bit, so that more relevant answers can be provided, but let me first mention Triangle, a 2D Delaunay generation tool, which is written in C, and can be used both as a standalone program, or called from your own code.
Then, about CGAL, here is a typical small example, in case you still consider it:
#include <vector>
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Delaunay_triangulation_2.h>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Delaunay_triangulation_2<K> Delaunay;
typedef K::Point_2 Point;
void load_points(std::vector< Point >& points)
{
points.push_back(Point(1., 1.));
points.push_back(Point(2., 1.));
points.push_back(Point(2., 2.));
points.push_back(Point(1., 2.));
}
int main()
{
std::vector< Point > points;
load_points(points);
Delaunay dt;
dt.insert(points.begin(), points.end());
std::cout << dt.number_of_vertices() << std::endl;
return 0;
}