Is it deer resistant?

Yes

Cenizo is deer resistant.

Leucophyllum frutescens

Deer: Rarely
Height: 12 ft (3.7 m)
Spread: 12 ft (3.7 m)
Zones: 8–12
Light: Full sun

Perennial
Shrub

Cenizo (Leucophyllum frutescens)

Photo: RandomKatze · CC0

Also called Purple Sage, Silverleaf, Texas Barometer Bush, Texas Ranger

Perennial Leucophyllum

More details

Light: Full sun, Partial shade
Water: Low
Type: Perennial, Shrub
Maintenance: Low
Growth: Medium
Bloom: Fall, Summer
Foliage: Evergreen
Features: Drought tolerant, Flowering
Best uses: Accent, Container, Foundation, Hedge