You can do it using the "collapse" directive: http://jsfiddle.net/iscrow/Es4L3/ (check the two "Note" in the HTML).
<!-- Note: set the initial collapsed state and change it when clicking -->
<a ng-init="navCollapsed = true" ng-click="navCollapsed = !navCollapsed" class="btn btn-navbar">
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</a>
<a class="brand" href="#">Title</a>
<!-- Note: use "collapse" here. The original "data-" settings are not needed anymore. -->
<div collapse="navCollapsed" class="nav-collapse collapse navbar-responsive-collapse">
<ul class="nav">
That is, you need to store the collapsed state in a variable, and changing the collapsed also by (simply) changing the value of that variable.
Release 0.14 added a uib-
prefix to components:
https://github.com/angular-ui/bootstrap/wiki/Migration-guide-for-prefixes
Change: collapse
to uib-collapse
.