Anyone can wear a Rosary. It is a wonderful aid for prayer that Christians have employed for over 800 years. In it is a summary of the Gospel in 3 groups of 15 "mysteries" regarding the life of our Lord, each of which bears a certain fruit:
The Annunciation: Humility
The Visitation: Charity
The Birth of Our Lord: Poverty, or detachment from the world
The Presentation of Our Lord: Purity of heart, obedience
The Finding of Our Lord in the Temple: Piety
The Agony in the Garden: Contrition for our sins
The Scourging at the Pillar: Mortification of our senses
The Crowning with Thorns: Interior mortification
The Carrying of the Cross: Patience under crosses
The Crucifixion and Death of Our Lord: That we may die to ourselves
The Resurrection: Conversion of heart
The Ascension: A desire for heaven
The Coming of the Holy Ghost: The Gifts of the Holy Ghost
The Assumption of our Blessed Mother into Heaven: Devotion to Our Lady
The Coronation of our Blessed Mother: Eternal happiness
On the Crucifix we pray the most ancient Profession of Faith of Christianity, the Creed of the Apostles. Other prayers include the Pater Noster (the prayer that the Lord taught us), the Gloria (Minor Doxology which in the current form exists since the fourth century), and the Angelic Salutation or Ave Maria (which is taken from the Scriptures but became known in its current form as an accepted universal prayer around the year 1050). The Salve Regina is also prayed at the very end (a beautiful hymn composed around 1080).
The Rosary (from Latin, "crown of roses") was given to Saint Dominic, founder of the Order of Preachers, in an apparition by the Virgin Mary in the year 1214. Probably one of the best books ever written on it is "The Secret of the Rosary" by Louis-Marie Grignon de Montfort (also author of the notorious "Treatise on the True Devotion", which covers the 3 legitimate Christian devotions to Mary and the 7 erroneous devotions).
If you are a Christian, you already are in partial communion with the Church, which is known since apostolic times to be one, holy, catholic, and apostolic, and which subsists in the Catholic Church governed by Peter's successor and the bishops in communion with him - meaning that ultimately there are no "non-catholic Christians": all the baptized are members of the mystical body of Christ, which is the Church ;).
Regardless, anyone can approach a priest or a deacon and ask him to bless a Rosary - which, in this way, becomes a sacramental dedicated solely to the praise of God and must be treated with somewhat greater care than other otherwise wordly objects (which is why Catholics sometimes don't like the idea of wearing them). But anyone can wear it, either blessed or not blessed, anyone can make one (which is a beautiful thought on your side), and anyone can use it.
If I may, I'd like to end with a quote from the Book of Revelation, 12, which, of the many parts of the Old and New Testament that speak of Mary, is perhaps the one that most beautifully shows the relationship of all Christians with her.
A great and wondrous sign appeared in heaven: a woman clothed with the sun, with the moon under her feet and a crown of twelve stars on her head.
She gave birth to a son, a male child, who will rule all the nations with an iron scepter. And her child was snatched up to God and to his throne.
The dragon was enraged at the woman and went off to make war against the rest of her offspring--those who obey God's commandments and hold to the testimony of Jesus.