#Re ou Ré au début d’un verbe ?
karmic linden
Nostradamus is off lol
Anyway, it's « rétrécir » because it's « r + étrécir »; think « rétablir (r + établir), réveiller (r + éveiller) ». « r– » is a shortened version of « re/ré– ».
Unfortunately this isn't a hard rule because you can have redoublings like « réépeler, réévaluer » so memorisation is the way to go
keen oxide
Rapetisser is also r + apetisser. Same for the verb rapiécer.
But yep, while there are rules, there are also exceptions to learn and memorize. Otherwise it wouldn't be French.
flint heron
This is what I read online:
In Old French (think 1000-1300, very roughly), you had two forms of re-: r- before vowels and re- elsewhere (seen today in verbs like rentrer from re- + entrer and your example of rejeter). By Middle French, a third form has arrived: ré-. Unlike the forms that came before it, which were neatly sorted between verbs starting with a vowel and those starting with a consonant, ré- can apparently show up before both consonants and vowels. We see examples of this new form as early as 1335, in the word réannexer. But when things are new, we don't always know exactly how or when to use them, so what would have been ralumer in Old French shows up as both rallumer and réallumer in Middle French, with the latter falling out of use in Modern French. Even today, you get some verbs showing up with different forms of the prefix, such as récrire and réécrire.
Ultimately, there is little chance for someone who does not already know the pronunciation of the word containing re- to look at the unaccented letters on the page and correctly determine whether to place the accent. The exceptions to this general guideline are 1) that I would expect that re- followed immediately by a vowel (not a - or a space) would carry the acute accent and 2) that when it is followed by a - or a space, I would expect no accent (and a native speaker could correct me here, because re- is usually only followed by a - or a space in informal writing, and I don't do a lot of informal writing in French to be able to have an instinct here).
Why is this so complicated 
is it really this complicated for french people?
flint heron
But yep, while there are rules, there are also exceptions to learn and memorize....
For example, would you write: Réécrire or Récrire ?
karmic linden
For example, would you write: Réécrire or Récrire ?
Not a native but I would write ||réécrire||
It should be noted that a lot of this is memorisation