I figured it out after all.
I had to create a pen object and set its line to round.
using (System.Drawing.Pen p = new System.Drawing.Pen(System.Drawing.Color.Black, fontSize * 0.3f))
{
p.LineJoin = System.Drawing.Drawing2D.LineJoin.Round;
g.DrawPath(p, path);
g.FillPath(System.Drawing.Brushes.White, path);
}