Make all text link

You could hook onto the latest_tweets_render_tweet filter and wrap the whole thing in a link

See theming in the Notes:
http://ww.wp.xz.cn/plugins/latest-tweets-widget/other_notes/#theming

However, I don’t recommend this.
The tweet itself will contain links, so personally I’d apply a JavaScript click handler to the tweet element and ensure it allows clicks on inner links to work.