Indeed, there is a way to do this, but like many other Algolia powered websites it will take some developer power.
You mention that you have Algolia search on a Magento 2 installation. This suggests you have already successfully indexed records to Algolia. Your data is ready and it can now be used anywhere you want.
On your external website, ask your development team to select their preferred InstantSearch library from these options here
You can now utilize an InstantSearch library searchBox widget in any website and use it to get results from your existing Algolia indices.
Hope this helps.