I’m going to give you a list of the best known gods and spirits associated with rats.
Ninkilim was a Mesopotamian deity associated with field pest, such as rodents and locusts. The name "Ninkilim" means "Lord Rodent," and the deity was the focus of rituals to protect crops from damage by vermin. In some texts, Ninkilim is depicted as a male god, while in others, a goddess.
The Greek god Arimanius is associated with rats, favoring them as his chosen animals.
This association is mentioned in Roman sources and is linked to the god's origins in the Zoroastrian deity of destruction, Ahriman.
Daikoku, the Japanese god of wealth and farmers, is associated with rats because they are seen as his benevolent companions and messengers, symbolizing prosperity and good fortune. The association stems from various factors, including the rat's connection to the sign of the Rat in the Chinese zodiac and its role in the mythology of Daikoku's syncretic origins.
Lord Ganesha is associated with a rat, called Mooshika, which serves as his vehicle (vahana) and symbolizes several key concepts, including the ability to overcome obstacles, control of desires and greed, and humility. The rat's symbolic meaning often refers to the control of insatiable desires or ego, representing Ganesha's power to conquer the self. Mythological stories also explain the rat as a demon named Gajmukhasur who was transformed into a mouse by Ganesha.
Tilalofonua is a god of the flying rat in Niuean mythology, also known as the god of the Kuma (rat and bird of the heavens). According to myth, Tilalofonua was denied wings by the flying fox god Halevao until he demonstrated his love, after which Halevao gave him wings to test.
Tesso is the “Iron Rat” of Japanese mythology, a powerful yokai that was once the Buddhist monk Raigō. He transformed into a giant rat with iron teeth and claws after dying of a hunger strike, fueled by rage when Emperor Shirakawa broke a promise to reward him for helping him have an heir. In his new form, he commanded an army of rats to attack the rival monastery Enryaku-ji.
There is no single Philippine god explicitly associated with rats, as pre-colonial animistic beliefs focused more on a general reverence for nature and spirits rather than specific animal deities. However, the animistic belief system may have led to the respectful or fearful treatment of rats, and some modern Filipinos continue to view rats as having spirits. For example, the practice of calling rats "mabait" (kind/good ones) may stem from the belief that being disrespectful to them could lead to negative consequences. Which reminds me of referring to fae or fairy as the kindly ones, the fair folk, or the good neighbors.
The following are not specifically referenced with rats but are associated with wild/nocturnal animals.
Hecate is strongly associated with wild animals, including being called the "mistress of beasts". She is most famously linked to dogs and snakes, but her associations also include horses, lions, wolves, and various others like boars, polecats, and even frogs. These animals often represent aspects of her domain over magic, the night, the underworld, and the liminal spaces where wildness and civilization meet. In my experience she likes rats.
Mictlantecuhtli is the Aztec god of death and ruler of the underworld, Mictlán. He is strongly associated with nocturnal animals such as bats, owls, and spiders, and a famous stone altar dedicated to him features carvings of these creatures. These animals were linked to the night, darkness, and the underworld, which was ruled by Mictlantecuhtli.
Cernunnos is the Celtic god of wild animals and places, fertility, and prosperity. He is also associated with nature, the hunt, the underworld, and the cycle of life and death, serving as a mediator between humans and the wild. He is famously depicted as a horned figure with the body of a man. Rats would fit into the areas he covers well.
Spiritually, rats symbolize resourcefulness, adaptability, survival, and intelligence particularly in navigating difficult situations. In some Eastern cultures, they are also seen as symbols of prosperity and good fortune. However, rats can also represent negative aspects like cunning, disease, and the "shadow self" in their association with the unseen or instinctive parts of life. With that in mind you could find other deities and spirits that might work with rats but aren’t historically listed as being associated with them.