Here are some clues from the book:
On page 10 (hardcover first edition), the prison guard asks him what race he is, asking if he's Hispanic or a Gypsy. The guard goes on to suggest that maybe he's part black. Later in the story, Sam thinks that he looks native American:
"You got Indian blood in you?"
"Not that I know of."
"You looked like it, was all."
Later there's a reference to his cream-and-coffee skin:
. . . here he was, a large, clumsy sixteen-year-old with acne pocking his cream-and-coffee skin . . .
When Shadow meets Mr. Nancy, it's stated that he has light grey eyes:
"You're a big one," said Nancy, staring into Shadow's light gray eyes . . .
And later when he sees himself as a child:
. . . a shrimp of a kid, big pale gray eyes and dark hair . . .
Although, confusingly, there are also suggestions that he might have dark eyes:
The only photograph of Shadow as a kid that Laura had liked enough to frame showed a solemn child with unruly hair and dark eyes . . .
"Damn your dark eyes, you gave it a-fucken-way."
A second reference to his dark hair:
He washed his face and hands in hot water, slicked down his dark hair, then went back into the restaurant and ate his burgers and fries and drank his coffee.
About Shadow's mother: a major clue is that she has sickle-cell disease, which occurs mostly in people of sub-Saharan African descent.
. . . what she had thought was just another sickle-cell crisis . . .
When she's sick,
There was a lemonish-gray tinge to her skin.
We eventually find out that Shadow's father is white, which means that the genes for his darker skin must have come from his mother.