There are rituals for summoning angels, not unlike demon summoning rituals. However, angel summoning rituals appear less commonly than their demonic counterparts. There are also rituals for summoning an archangel.
As with demon summoning rituals, there are many variations, some simpler or more complex than others.
Summoning an Archangel
Summoning an archangel requires an enochian chant to be recited. Other requirements appear to vary.
In Free To Be You and Me, Castiel performed a summoning ritual to summon Raphael. Castiel performed this on Donnie, Raphael's original vessel. Although used on an archangel, Castiel described the method somewhat similar to dialing to access an 'open phone line' between a 'vessel and his angel'. This could mean that it could work on regular angels as well.
When summoning Raphael, Castiel uses a simple ritual. An Enochian incantation to summon Raphael later recited:
Rah ah gah ee oh es
Vee nu nohno kee ah seh peh teh poh ah ma lah deh zod
In Point of No Return, however, Zachariah uses different Enochian incantation to summon Michael to Earth. Strangely, Zachariah just simply reciting the spell to summon Michael, and no any form of ritual was held. An Enochian incantation to summon Michael is:
Zod ee reh doh noh koh ah beh rah ma geh nah zod peh sah geh
In Hell's Angel, Dean summoned Lucifer using various ingredients and an incantation which he read from a scroll. This summoning ritual allowed Lucifer to receive messages from Dean, such as the promise of a Hand of God.
Summoning an Angel
A bowl or dish filled with various materials, most of them akin to leaves, herbs or petals set before a circular sigil. The sigil itself is separated by four lines into four areas or quadrants. Each quadrant contains a different enochian symbol or letter.
Outside the circle, four other enochian symbols are written. Four lit candles are placed atop the four quadrants, and four other objects are placed at the farthest points outside the circle. A trinket placed near the dish is also required. To complete the ritual, the summoner must set the materials in the dish on fire. Once the materials are lit, the angel appears instantaneously in the immediate vicinity. Unlike demon summoning, the ritual to summon angels did not require an incantation.