You can pray to your guardian angel, just as you can pray to any saint. It is important to note that this is not an act of worship, but of the honor due to the ministers of God sent to serve our salvation (Heb. 1:14).
Indeed, Scripture shows that the appeal to God bears fruit in the mediation and help of the angels, whether it was Abraham’s appeal for Sodom, ultimately unfruitful due to human obstinacy in sin, or Tobit’s appeal for healing, which resulted in the sending of St. Raphael to help him and his family. St. Raphael’s mediation of the divine will is shown to be direct, immediate and personal. The intercessory role of Raphael is also shown, when he reveals,
I am Raphael, one of the seven holy angels who present the prayers of the saints and enter into the presence of the glory of the Lord. (Tobit 12:15)
This important intercessory role is further shown in the New Testament in Rev. 8:3-4.
And another angel came and stood at the altar with a golden censer; and he was given much incense to mingle with the prayers of all the saints upon the golden altar before the throne; and the smoke of the incense rose with the prayers of the saints from the hand of the angel before God.
Following Scripture and Tradition, therefore, popes and saints have encouraged Christians to seek the help of their angels through prayer. As St. Bernard of Clairvaux said, “We should show our affection for the angels, for one day they will be our co-heirs, just as here below they are our guardians and trustees appointed and set over us by the Father.”