$ cat /tmp/bash-test ; /tmp/bash-test foo
#!/bin/bash

if (( $1 >= 0 )) 2>/dev/null; then
echo "Argument '$1' is integer"
fi

Argument 'foo' is integer

I've used bash's regex support to test for an integer when I was handling options, e.g.:

if [[ $1 =~ ^[0-9]+$ ]] && [[ $1 -gt 0 ]]; then
echo "Argument '$1' is integer"
fi