Hello Welcome to the Forums,
Here is the code,
if (site == SPSite("<SharePoint URL>"))
{
SPWeb web = site.OpenWeb();
if (web != null)
{
SPList list = web.Lists["Wiki Pages"];
SPListItem item = list.Items[1];
string mycontent = item["Wiki Content"].ToString();
//add new link
mycontent += "<div><a class=ms-wikilink href=\"<Link of the home page\">Home</a></div>";
item["Wiki Content"] = mycontent;
item.Update();
}
}