Can FileMaker communicate with another website's service api?

I am very unfamiliar with APIs in general. In my specific example, a website file hosting service called "SmartFile" (much like Dropbox) offers an API where I can download my activity log from my account:

https://app.smartfile.com/api/2/activity/

can anyone offer some insight as to how I could import data into FileMaker via this API offered?

They say they support json as well as xml. Any help pointing me in the right direction is much appreciated. 

Yes, there are many third party tools that can submit json or https post requests even FMP 13 can do these however the plugins can perform more function that are limited in FMP

http://www.restfm.com

http://www.goya.com.au/baseelements/plugin

http://360works.com/web-services-manager/

http://360works.com/scriptmaster/

http://www.scodigo.com/smartpill2-now-available

http://www.seedcode.com/dropbox-to-filemaker/

Can FileMaker communicate with another website's service api?

The answer depends on the specific API. If the API (1) responds to one of the HTTP requests that Filemaker can make, and (2) returns an XML document in response, then you can import the response directly using (3) a custom XSLT stylesheet to transform the response into Filemaker's own XML grammar. In this scenario, with all 3 conditions satisfied, no plugins are required.