I found the following solution:
using Microsoft.VisualStudio.VCProjectEngine;
using Microsoft.VisualStudio.Shell.Interop;
//...
EnvDTE.DTE dte = (EnvDTE.DTE)Microsoft.VisualStudio.Shell.Package.GetGlobalService(typeof(SDTE));
VCProject prj = (VCProject)dte.Solution.Projects.Item(1).Object;
VCFilter filter = prj.AddFilter("Custom Filter");
filter.AddFile("D:\\path\\File.h");
prj.Save();
Also you need to add Reference to Microsoft.VisualStudio.VCProjectEngine.