Is there any way for ReactJS to send an HTTP request?

No.And this is a good thing.

Most work arounds are now blocked by the major browsers, and as you state you will encounter mixed content issues. Firefox was the last to implement this by default and you can see there documentation here.

For those who are unaware of dangers of mixed content the following article gives a reasonable overview: howtogeek. While you state that you feel that as you are encrypting the mobile numbers with AES and that is fine, I suggest you reconsider. Cracking a mobile number is much easier than cracking a password (but don't send those either!) in general and is a key component of identity theft, regardless of whether it can be obtained in other ways.

In my view the correct way to approach this to have the user authenticate normally.

I have included a snippet from rfc2616-sec15 below, I believe it is relevant and encourage you again to consider an alternative.

HTTP clients are often privy to large amounts of personal information(e.g. the user's name, location, mail address, passwords, encryptionkeys, etc.), and SHOULD be very careful to prevent unintentionalleakage of this information via the HTTP protocol to other sources. Wevery strongly recommend that a convenient interface be provided forthe user to control dissemination of such information, and thatdesigners and implementors be particularly careful in this area.History shows that errors in this area often create serious securityand/or privacy problems and generate highly adverse publicity for theimplementor's company.