I'm searching for short English texts to memorize. Provided that it has: rhyme and assonance easy to repeat (Like:If— by Rudyard Kipling).My experience in learning my mother tongue Arabic in addition to Hebrew using passages from sacred texts and prayers was excellent. Can someone help me in this matter? The texts may be: verses from the Bible, a short poem, a prose sermon, proverbs, etc. It is preferable to have an audio reading on the net, and to contain noble and sublime meanings.
Short rhymed texts... ie poems.
There are plenty of English poets. Pick one! How about Tennyson?
On the other hand, bible texts are rarely rhymed, and have usually lost their meter in translation. Most Psalms, for example, are translated to prose to preserve the meaning, not the song. Sermons are nearly always prose, as are most proverbs.
You could try browsing audio book sites such as Amazon Kindle (other audio book sites are available - some with free downloads). There are hundreds of audio books related to the bible and as many books of poetry or any other topic that interests you. You should probably stick with modern versions as you do not want to learn archaic language forms.
For example, you mentioned If by Rudyard Kipling I noticed that 3 free versions of this are available on a site called digitalbook.io along with many other classic English texts. The only 2 downsides of this site that I can see is that it is audio only ( you would have to get the printed version elsewhere if you wanted it) and the narrators I listened to are speaking with American accents, but that may not be a disadvantage to you.
Since we don't know your current level of English ability, it is almost impossible to recommend suitable books. You might need to start with anything from Michael Rosen (a very popular children's poet) to the works of Shakespeare which even some native speakers find difficult.