AFAIK, there is no such ootb login component you can just include in your page component, but it is easy to create one by yourself. You can take reference from any sample sites We.Retail (for 6.3) or Geometrixx Outdoor (for 6.2).
/apps/weretail/components/structure/page is the page component for We.Retail. It has reference to /apps/weretail/components/structure/header and header.html file includes /apps/weretail/components/structure/header/include.html. Link of login and logout is mentioned in this include.html, and path of sign in and logout page is defined in /apps/weretail/components/structure/header/Header.java. Login page is referred as /content/we-retail/us/en/community/signin and it contains login component having resourcetype as social/console/components/hbs/login. Most of these components are written in sightly but login component from social is in handlebars.