For those who has the same issue or will ever have...

Not sure if it's the best way, but i've created new instance of UmbracoHelper and that helped:

UmbracoHelper helper = new UmbracoHelper(umbPage, Umbraco.TagQuery, _dicFactory, _compRenderer, Umbraco.ContentQuery, Current.UmbracoHelper.MembershipHelper);

where _dicFactory and _compRenderer are injected to existing api controller...

public UmbracoContentApiController(ICultureDictionaryFactory dicFactory, IUmbracoComponentRenderer compRenderer)
        {
            _dicFactory = dicFactory;
            _compRenderer = compRenderer;
        }

Then you can easily render macro using:

var macro = helper.RenderMacro("MacroAlias");