But I don't wanna use a picture on LinkedIn

For LinkedIn to be at 100% compete you need a picture, and if you are not at 100%, LinkedIn will not be optimized.A photo is essential especially if you are job searching or open to new opportunities.Your picture allows people to connect with you--even if only subliminally. Not having a photo is like saying, "How I dress shouldn't matter." Linked In is about personal branding--and so is job seeking.

SCS reader says:

LinkedIn Profile Picture vs. Resume Picture

It is widely advised that applicants should NOT put their picture on their resume, however applicants are being advised to put there LinkedIn profile on there resume, which most of them have a picture. For individuals who do not want to be discriminated against, is it a good idea to advise them to not put there LinkedIn profile on there resume or remove the picture from their profile?
 
SCS Answer

No, I do not think you should advise to have no picture, as long as the picture is professional. The resume is a document, that is often scanned into ATS so a picture would not be ideal. The Linkedin profile is just that, a profile. I see it as a passport to get you to where you want to be and shows where you have been. Having no picture will hurt most candidates, no matter how well their profile is written. (this coming from the majority of employers I have spoken to) because without a picture your profile is incomplete.