Robin Paone the embed map in ArcGIS Online doesn't have a time option. However you can share your web map using the Time Aware template and then embed that into your website using an Iframe.
The Time Aware template was designed to be highly configurable so you can enable options like a legend, title, color scheme etc making it easy for you to customize it to match the look of the web site you want to embed the app into. You can find the Time template by opening your time-aware web map in the ArcGIS Online Map Viewer then click Share > Create a Web App then browse through the gallery to find Time Aware then choose create. After selecting create you'll have the option to customize the look and behavior of the template. Once done you can copy the app url and insert it into an iframe which can then be embedded into your existing site:
HTML iframe tag
