Yes, the two triangles are similar.
Similar triangles have equal corresponding angles and proportionate sides.
We can see that the corresponding angles of the two triangles are equal because although the smaller triangle is rotated, the angle measurements of both triangles are 23°, 67°, and 90°.
The corresponding sides are proportionate because they have a set ratio. The sides of the smaller triangle are all 1/4 the length of the corresponding sides of the bigger triangle.