Yes there is way to earn crypto currency without any investment that is by participate in

Airdrop

Bounty program

Airdrop is a promotional marketing strategy which is opted by the most of the ICO to create the market hype and to enahr the community. Usually in order to participate you just have to join Telegram channel of respective ICO and by liking the social handles but it can also vary from ICO to ICO.

Bounty Program is another way of creating the market hype and engaging the community for the longer time period. In bounty program you have to promote ICO on your social handles, in depends on the participants, in which (s)he is interested. Generally it includes promotion on Facebook, Twitter ,BTT, Reddit and Medium