Copy and paste the following script.
<script language="ecmascript" type="text/ecmascript">
        var fieldCollection;
        var field;
        var list;
        function fieldRequired() {
            var clientContext = SP.ClientContext.get_current();
            if (clientContext != undefined && clientContext != null) {
                var webSite = clientContext.get_web();
                this.list = webSite.get_lists().getByTitle("List Request");
                this.fieldCollection = list.get_fields();
                this.field = fieldCollection.getByTitle("Date");
                this.field.set_required(true);
                this.field.update();
                clientContext.load(this.field);
                clientContext.executeQueryAsync(Function.createDelegate(this, this.OnLoadSuccess), Function.createDelegate(this, this.OnLoadFailed));
            }
        }
        function OnLoadSuccess(sender, args) {
            alert(this.field.get_required());
        }
        function OnLoadFailed(sender, args) {
            alert('Request failed. ' + args.get_message() + '\n' + args.get_stackTrace());
        }</script>
    <input id="btnFieldRequired" onclick="fieldRequired()" type="button" value="Set Required Field" />