sure, the social groups module exposes this via a services framework method so typically that's how you would do so (you can see the relevant code in the groups module). If you want to do it via code directly then just take a look at the code in DNN Platform\Modules\Groups\ModerationServiceController.cs specifically the JoinGroup method

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Here it goes an example on how to do it...

var groupInfoList = RoleController.GetRoleGroups(this.PortalId);
foreach (RoleGroupInfo item in groupInfoList)
{
if (item.Roles.ContainsKey(groupName))
{
RoleController.AddUserRole(userInfo, item.Roles[groupName], this.PortalSettings, RoleStatus.Approved, DateTime.Now, DateTime.MaxValue, false, false);
}
}