Is there any online server to upload recommendation letters and share the link with the universities
In mathematics there is, and it is used by most research-oriented departments for hiring: MathJobs. Hiring departments pay (i.e., not candidates) and candidates indeed cannot view the recommendation letters.

It is extremely efficient, and in my opinion this system deserves to be more widely imitated. Note however that this is used at the option of the hiring department, and not the job candidate. So in particular you can't use this system, except for positions advertised via this site.

In your situation you might be able to use Interfolio, but I'd check with prospective employers (or your advisor) before using this.